So psalms is referring to an individual who will be serving as a king of justice, not a priest-king. The reason I say "king of justice" is because, while Christians commonly translate the term מלכי צדק as מלכיצדק Malkitzedek, that is, as a name, in reality there's a space between the two words and translated they mean "my king (of) justice".
The name Melchizedek means: "King of righteousness."
And Melchizedek was the king and priest of Salem. Now Salem means peace. So Melchizedek, king of Salem also means: King of peace.
Salem is the same area that David founded the city of Jerusalem. And Jerusalem means possession (or foundation) of twofold peace.
Paul, speaking of this prophecy, said:
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For this Mel·chizʹe·dek, king of Saʹlem, priest of the Most High God, met Abraham returning from the slaughter of the kings and blessed him, 2 and Abraham gave him a tenth of everything. First, his name is translated “King of Righteousness,” and then also king of Saʹlem, that is, “King of Peace.” 3 In being fatherless, motherless, without genealogy, having neither a beginning of days nor an end of life, but being made like the Son of God, he remains a priest for all time."-Hebrews 7:13.
Since nothing is recorded in the Biblical record about Melchizedek he is left without geneology. He typified, or represented the Messiah to come. It is speculated by some that he may have been Shem, the son of Noah. In any case he was apointed by Jehovah God himself as priest. And Abram gave tithes to him. Considering this fact Paul continues:
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True, according to the Law, those of the sons of Leʹvi who receive their priestly office have a commandment to collect tithes from the people, that is, from their brothers, even though these are descendants of Abraham. 6 But this man who did not trace his genealogy from them took tithes from Abraham and blessed the one who had the promises. 7 Now it is undeniable that the lesser one is blessed by the greater. 8 And in the one case, it is men who are dying who receive tithes, but in the other case, it is someone of whom witness is given that he lives. 9 And it could be said that even Leʹvi, who receives tithes, has paid tithes through Abraham, 10 for he was still a future descendant of his forefather when Mel·chizʹe·dek met him."-Hebrews 7:5-10.
Well Paul argues it better than I can. I was using the Bible in my first post to explain how the Messiah was to be a priest. The OP totally ignored it and said that David was calling himself his own lord, even though David himself said:
"Jehovah declared to my Lord:
“Sit at my right hand."
Jehovah declared to David's Lord, "Sit at my right hand." Jehovah's right hand is in heaven. David's Lord is greater than David.
The OP said Psalm 2 called David "son of God." But nowhere in scripture is David or any other human offspring of Adam called "son of God." The sons of God are angels. And Jehovah's firstborn son whom became known as Jesus Christ is in heaven sitting at God's right hand. He is David's Lord. He is also the Christ.
Again, I was using Paul's own arguments with the Hebrews with you:
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And this becomes even clearer when another priest arises who is like Mel·chizʹe·dek, 16 who has become such, not by the legal requirement that depends on fleshly descent, but by the power of an indestructible life. 17 For it is said in witness of him: “You are a priest forever in the manner of Mel·chizʹe·dek.”So, then, the former commandment is set aside because it is weak and ineffective. 19 For the Law made nothing perfect, but the introduction of a better hope did, through which we are drawing near to God. 20 Also, inasmuch as this was not done without an oath being sworn 21 (for, indeed, there are men who have become priests without a sworn oath, but this one has become so through an oath sworn respecting him by the One who said: “Jehovah has sworn, and he will not change his mind, ‘You are a priest forever’”), 22 Jesus has accordingly become the guarantee of a better covenant. 23 Furthermore, many had to become priests in succession because death prevented them from continuing as such, 24 but because he continues alive forever, his priesthood has no successors. 25 So he is able also to save completely those who are approaching God through him, because he is always alive to plead for them."-Hebrews 7:15-25.
The reason Jesus was accorded a priesthood greater than that of Aaron is made clear when we see that even the priests themselves had to offer animal sacrifices, first for themselves, and then for the rest of the people, and many times. Yet the sacrifice of the Messiah, his perfect life blood, was given once and for all times.
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For it is fitting for us to have such a high priest who is loyal, innocent, undefiled, separated from the sinners, and exalted above the heavens. 27 Unlike those high priests, he does not need to offer up sacrifices daily, first for his own sins and then for those of the people, because he did this once for all time when he offered himself up. 28 For the Law appoints as high priests men who have weaknesses, but the word of the oath sworn after the Law appoints a Son, who has been made perfect forever."-Hebrews 7:26-28.
Now this is the main point of what we are saying: We have such a high priest as this, and he has sat down at the right hand of the throne of the Majesty in the heavens, 2 a minister of the holy place and of the true tent, which Jehovah set up, and not man. 3 For every high priest is appointed to offer both gifts and sacrifices; so it was necessary for this one also to have something to offer. 4 If he were on earth, he would not be a priest, since there are already men who offer the gifts according to the Law. 5 These men are offering sacred service in a typical representation and a shadow of the heavenly things; just as Moses, when about to construct the tent, was given the divine command: For He says: “See that you make all things after their pattern that was shown to you in the mountain.” 6 But now Jesus has obtained a more excellent ministry because he is also the mediator of a correspondingly better covenant, which has been legally established on better promises.
That last quote is from Hebrews 8:1-6.