The author of Hebrews is not using outside texts to make his arguments in ch 7 , where he explains how Yahuwshuwa HaMashiyach (Jesus Christ) fulfills Psalm 110 as being the Priest forever after the order of Melchisedec. Melchisedec is a very important person in the Old testament, even though only few verses are written about him. Since you talked about the first three verses, we will break them down. All throughout the book of Hebrews the author uses the Hebrew scriptures to prove his points about Yahuwshuwa and the new covenant. Every argument he uses is straight from the scriptures and can be checked by anybody, he doesn't bring any arguments from secret sources outside the scriptures. he is writing to Hebrew people using the Hebrew scriptures to prove Yahuwshuwa is the Hebrew Messiah. So anyone there with the scriptures can follow along with the author.
in Hebrews ch 7 the Author is making an argument from genesis 14:17-24:
17 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.
18 And Melchizedek king of Salem brought forth breadand wine: and he was the priest of the most high God.
19 And he blessed him, and said, Blessed be Abram of the most high God, possessor of heaven and earth:
20 And blessed be the most high God, which hath delivered thine enemies into thy hand. And he gave him tithes of all.
21 And the king of Sodom said unto Abram, Give me the persons, and take the goods to thyself.
22 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,
23 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:
24 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.
He is using these verses to prove that Yahuwshuwa fulfills Psalm 110:
Psalm 110 (KJV)
1 The Lord said unto my Lord, Sit thou at my right hand, until I make thine enemies thy footstool.
2 The Lord shall send the rod of thy strength out of Zion: rule thou in the midst of thine enemies.
3 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.
4 The Lord hath sworn, and will not repent, Thou art a priest for ever after the order of Melchizedek.
5 The Lord at thy right hand shall strike through kings in the day of his wrath.
6 He shall judge among the heathen, he shall fill the places with the dead bodies; he shall wound the heads over many >countries.
7 He shall drink of the brook in the way: therefore shall he lift up the head.
Every thing the author of the book of Hebrews is using in Hebrew Ch.7 can be found in these verses from genesis 14 and psalm 110, which are the only times Melchisedec is mentioned in the scriptures.
the Author is trying to show the similarities between Melchisedec and Yahuwshuwa.
Here are the first 3 verses of Hebrew 7:
Hebrews 7 (KJV)
1 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;
2 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;
3 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.
In verse 1 the author introduces who Melchisedec is according to the scriptures, a king and priest of Salem who met Abraham returning from his victory against the kings.
In verse 2 the authors tells us about the tithe Abraham gave to Melchisedec, then interprets the name of melchisedec as meaning king of righteousness, then he interprets king of Salem as meaning king of Peace. He is doing this to connect it to Yahuwshuwa who is also king of righteousness and peace, who is also above Abraham.
So far everything he has been saying has been from Genesis 14 to prove Psalm 110. Nothing changes in verse 3 and the rest of the chapter.
In verse 3 it says Melchisedec is without father, mother, descent, having no beginning of days or end of life. So what was meant by this? there are all kinds of crazy theories about who Melchisedec is because of this verse. But again the author is not using any secret sources, he is using the scriptures for people to follow along his arguments.
Genealogy is Very important to the Hebrew people, its made evident through the extensive geneologies recorded and preserved. We can see the birth, amount of years lived, the fathers, and the death of the bloodline of Seth going to Noah is Genesis 5. we see their "father, descent, beginning of days, and their end of life" recorded for all to see. Then we can go to Genesis 11:27 and see the birth of Abram ( Abraham), and his father being Terah. Then in Ch 25 we can read about his death and how many years he lived. We can do the same thing for Isaac, Jacob, Esau, Moses, Aaron, Samuel, David, and all the kings of Judah and Israel. We can go to each of these men and find their birth recorded, how many years they lived, their death, who their fathers were, and most of them we can read about who their mothers were. Its all there for us to read.
BUT when we go to Genesis 14, Melchisedec pops in out of nowhere. And he has such an high status that even Abraham paid a tithe to him and was blessed by him. But nothing is recorded about his birth, death, or parents, which is very unusual in the scriptures for a man of such high status even above Abraham. But what the author is Hebrews is trying to show us is, that the genealogy was purposely left out, by inspiration of the Holy Spirit, to symbolically represent and prophecy the everlasting Priesthood that would come after the order of this man, which would be above the Order of Aaron, since the levites paid tithes through Abraham their father to Melchisedec ( Heb 7:9). This is why his birth or death is not recorded. Then the rest of Hebrews 7 continues to use genesis 14 and psalm 110 to show all the similarities between Melchisedec's and Yahuwshuwa's priesthood