The order of Melqe Tsedeq (or Malkiy Tsedeq) is the order of Melchizedek, which is One with the order of Nyahbinghi. Malkiy Tsedeq is the Hebrew spelling. In regards to the Tewado Hymanot (or Tewahdo haymanot). Tewahdo is a Ge'ez word meaning "being made one". Some say Haymanot means "the Father, the Son and the Holy Spirit." while others say it means faith. These words are sometimes used in reference to the Ethiopian Church.
You see, when some people speak, they purposely say things in a way where many won't Iverstand what they are speaking. Their interest is in making themselves appear intelligent and versed instead of educating people. So instead of saying something in the common way that most will Iverstand, or at least providing a translation or explanation to what they said, they will say it a different way in an attempt to exalt themselves over others based on their "knowledge".
The prayer Teff is refering to is the prayer that Christ taught.
sime yiQedes mengisthi timTa,
feQadih besemay indehonech,
indyhum bemdr tihun.
Yeilet injerachinin siTen zare,
Bedelachininim yiQir bilen,
ińa yebedelunin yiQir indeminil.
Wede fetenam atagiban,
kekifu hulu adinen inji,
mengist yante nat ina hail misganam lezelalemu,
Matthew 6 (also Luke 11)
 After this manner therefore pray ye: Our Father which art in heaven, Hallowed be thy name.
 Thy kingdom come. Thy will be done in earth, as it is in heaven.
 Give us this day our daily bread.
 And forgive us our debts, as we forgive our debtors.
 And lead us not into temptation, but deliver us from evil: For thine is the kingdom, and the power, and the glory, for ever. Amen.
I and I are not meant to be limited by this prayer, Christ was teaching people to not pray as the pharisees, with vain repetitions and praying in front of people to exalt yourself. He said to pray "After this manner", so this means to pray "in this way", or "in a similar way", but I and I can speak our own prayers. Prayer is I and I communication to Jah RasTafarI, so speak to Jah about anything you need to speak about.
Here is a prayer from Haile Selassie I.
O Lord, almighty in whom there is no weakness, eternal in whom there is no transience; in admiring Your work as well as Your judgements, a created being, even after much searching, cannot fathom them—except to a limited extent.
It is a subtle secret which a creature, even after much exploring, cannot know but which You alone do know: why in the immediate past as well as now You have made the Ethiopian people, from the ordinary man to the Emperor, sink in a sea of distress for a time, and why You have made the Italian people up to its King swim in a sea of joy for a time.
Since no creature created in Your image and to Your pattern gives up hope that everything he begs of You will be done for him until the day You sever his soul from his body, we beseech You that Ethiopia should not remain with her freedom extinct and prostrate under an alien ruler, so that the mouth of her peoples be silenced for fear of a foreign governor, but rather that You will save them by Your deeds of kindness, lest they remain with their hearts oppressed through being deprived of their own Ethiopian ruler who was leading them towards civilization under a light yoke and with gladness.
O Lord, abode of exiles, light of the blind! Truth and justice are Your thrones. Receive us who have been exiled for our freedom's sake, who have had to leave our country on account of violent assault. In praying to You thus, it is not for our righteousness but for Your great mercies.
And now I am setting out contemplating to write the story of my life from my thirteenth year until this time, on the basis of what You have wrought, making me Your instrument. I pray to You that it may be Your will to let it reach completion. It is right for me to reveal in this preface the reason why I have thought to write this, although from You nothing is hidden.
First, that Your name be praised for all the deeds You do, acting according to Your wishes.
Second, when You make a man rich in the honours of this world and appoint him above other creatures, that it be known that it is not for his merit but only through Your benevolence and generosity.
Third, in every line in this history, where the name of another person is mentioned, it is not through partiality or enmity—save in error—but You know that we are making our heart the judge to write only the truth.
Fourth, although there is nothing that is not written in the Holy Scriptures, if You will enable me to write as I have planned, may our kin and our brothers who will rise up in future take note of the word You have spoken 'for without me you can do nothing' and may their hearts be convinced that with Your help alone will they be able to do anything.
Fifth, unless a man discharges his task by his own resolve and perseverance conscious of being Your tool, whether in times of joy or tribulation, he should realize that he ought to work by his innate ability or by such education as he may have acquired, for his responsibility will not cease even if he acts solely under another man's will.
Sixth, whatever the task may be, let everyone realize and be convinced that it will be accomplished at the proper time and age and that it is impossible to have it fulfilled either by just desiring it or by hurrying it unduly.
I pray to You that all this may be in full accord with Your will.
Here a few places in the scriptures where it refers to Melchizedek.
 And when Abram heard that his brother was taken captive, he armed his trained servants, born in his own house, three hundred and eighteen, and pursued them unto Dan.
 And he divided himself against them, he and his servants, by night, and smote them, and pursued them unto Hobah, which is on the left hand of Damascus.
 And he brought back all the goods, and also brought again his brother Lot, and his goods, and the women also, and the people.
 And the king of Sodom went out to meet him after his return from the slaughter of Chedorlaomer, and of the kings that were with him, at the valley of Shaveh, which is the king's dale.
 And Melchizedek king of Salem brought forth bread and wine: and he was the priest of the most high God.
 And he blessed him, and said, Blessed be Abram of the most high God, possessor of heaven and earth:
 And blessed be the most high God, which hath delivered thine enemies into thy hand. And he gave him tithes of all.
 And the king of Sodom said unto Abram, Give me the persons, and take the goods to thyself.
 And Abram said to the king of Sodom, I have lift up mine hand unto the LORD, the most high God, the possessor of heaven and earth,
 That I will not take from a thread even to a shoelatchet, and that I will not take any thing that is thine, lest thou shouldest say, I have made Abram rich:
 Save only that which the young men have eaten, and the portion of the men which went with me, Aner, Eshcol, and Mamre; let them take their portion.
 The LORD said unto my Lord, Sit thou at my right hand, until I make thine enemies thy footstool.
 The LORD shall send the rod of thy strength out of Zion: rule thou in the midst of thine enemies.
 Thy people shall be willing in the day of thy power, in the beauties of holiness from the womb of the morning: thou hast the dew of thy youth.
 The LORD hath sworn, and will not repent, Thou art a priest for ever after the order of Melchizedek.
 The Lord at thy right hand shall strike through kings in the day of his wrath.
 He shall judge among the heathen, he shall fill the places with the dead bodies; he shall wound the heads over many countries.
 He shall drink of the brook in the way: therefore shall he lift up the head.
 For every high priest taken from among men is ordained for men in things pertaining to God, that he may offer both gifts and sacrifices for sins:
 Who can have compassion on the ignorant, and on them that are out of the way; for that he himself also is compassed with infirmity.
 And by reason hereof he ought, as for the people, so also for himself, to offer for sins.
 And no man taketh this honour unto himself, but he that is called of God, as was Aaron.
 So also Christ glorified not himself to be made an high priest; but he that said unto him, Thou art my Son, to day have I begotten thee.
 As he saith also in another place, Thou art a priest for ever after the order of Melchisedec.
 Who in the days of his flesh, when he had offered up prayers and supplications with strong crying and tears unto him that was able to save him from death, and was heard in that he feared;
 Though he were a Son, yet learned he obedience by the things which he suffered;
 And being made perfect, he became the author of eternal salvation unto all them that obey him;
 Called of God an high priest after the order of Melchisedec.
 Of whom we have many things to say, and hard to be uttered, seeing ye are dull of hearing.
 For when for the time ye ought to be teachers, ye have need that one teach you again which be the first principles of the oracles of God; and are become such as have need of milk, and not of strong meat.
 For every one that useth milk is unskilful in the word of righteousness: for he is a babe.
 But strong meat belongeth to them that are of full age, even those who by reason of use have their senses exercised to discern both good and evil.
 For when God made promise to Abraham, because he could swear by no greater, he sware by himself,
 Saying, Surely blessing I will bless thee, and multiplying I will multiply thee.
 And so, after he had patiently endured, he obtained the promise.
 For men verily swear by the greater: and an oath for confirmation is to them an end of all strife.
 Wherein God, willing more abundantly to shew unto the heirs of promise the immutability of his counsel, confirmed it by an oath:
 That by two immutable things, in which it was impossible for God to lie, we might have a strong consolation, who have fled for refuge to lay hold upon the hope set before us:
 Which hope we have as an anchor of the soul, both sure and stedfast, and which entereth into that within the veil;
 Whither the forerunner is for us entered, even Jesus, made an high priest for ever after the order of Melchisedec.
 For this Melchisedec, king of Salem, priest of the most high God, who met Abraham returning from the slaughter of the kings, and blessed him;
 To whom also Abraham gave a tenth part of all; first being by interpretation King of righteousness, and after that also King of Salem, which is, King of peace;
 Without father, without mother, without descent, having neither beginning of days, nor end of life; but made like unto the Son of God; abideth a priest continually.
 Now consider how great this man was, unto whom even the patriarch Abraham gave the tenth of the spoils.
 And verily they that are of the sons of Levi, who receive the office of the priesthood, have a commandment to take tithes of the people according to the law, that is, of their brethren, though they come out of the loins of Abraham:
 But he whose descent is not counted from them received tithes of Abraham, and blessed him that had the promises.
 And without all contradiction the less is blessed of the better.
 And here men that die receive tithes; but there he receiveth them, of whom it is witnessed that he liveth.
 And as I may so say, Levi also, who receiveth tithes, payed tithes in Abraham.
 For he was yet in the loins of his father, when Melchisedec met him.
 If therefore perfection were by the Levitical priesthood, (for under it the people received the law,) what further need was there that another priest should rise after the order of Melchisedec, and not be called after the order of Aaron?
 For the priesthood being changed, there is made of necessity a change also of the law.
 For he of whom these things are spoken pertaineth to another tribe, of which no man gave attendance at the altar.
 For it is evident that our Lord sprang out of Juda; of which tribe Moses spake nothing concerning priesthood.
 And it is yet far more evident: for that after the similitude of Melchisedec there ariseth another priest,
 Who is made, not after the law of a carnal commandment, but after the power of an endless life.
 For he testifieth, Thou art a priest for ever after the order of Melchisedec.
 For there is verily a disannulling of the commandment going before for the weakness and unprofitableness thereof.
 For the law made nothing perfect, but the bringing in of a better hope did; by the which we draw nigh unto God.
 And inasmuch as not without an oath he was made priest:
 (For those priests were made without an oath; but this with an oath by him that said unto him, The Lord sware and will not repent, Thou art a priest for ever after the order of Melchisedec:)
 By so much was Jesus made a surety of a better testament.
 And they truly were many priests, because they were not suffered to continue by reason of death:
 But this man, because he continueth ever, hath an unchangeable priesthood.
 Wherefore he is able also to save them to the uttermost that come unto God by him, seeing he ever liveth to make intercession for them.
 For such an high priest became us, who is holy, harmless, undefiled, separate from sinners, and made higher than the heavens;
 Who needeth not daily, as those high priests, to offer up sacrifice, first for his own sins, and then for the people's: for this he did once, when he offered up himself.
 For the law maketh men high priests which have infirmity; but the word of the oath, which was since the law, maketh the Son, who is consecrated for evermore.
from the Kebra Negast:
105. Concerning the belief of ABRAHAM
And thou dost not understand that they were justified by faith-ABRAHAM, and DAVID and all the Prophets, one after the other, who prophesied concerning the coming of the Son of God. And ABRAHAM said, "Wilt Thou in my days, O Lord, cast Thy word upon the ground?" And God said unto him, "By no means. His time hath not yet come, but I will shew thee a similitude of His coming. Get thee over the JORDAN, and dip thyself in the water as thou goest over, and arrive at the city of SÂLĘM, where thou shalt meet MELCHIZEDEK, and I will command him to show thee the sign and similitude of Him." And ABRAHAM did this and he found MELCHIZEDEK, and he gave him the mystery of the bread and wine,2 that same which is celebrated in our Passover for our salvation through our Lord JESUS CHRIST. This was the desire and the joy of ABRAHAM as he went round the altar which MELCHIZEDEK had made, carrying branch and palm on the day of the Sabbath. See how he rejoiced in his belief, and see how he was justified by his belief, O blind JEW, who though having eyes seest not, and having ears hearest not, even as the Prophet ISAIAH saith concerning you, "Their eyes are blind, and their hearts are covered with darkness, so that they may not understand and God may not show compassion unto them."
Here are a couple of places where Melchizedek is reasoned about.
Till Shiloh Come
Haile Selassie I