Here are links to part 1 and part 2. I am quoting the same verses multiple times in this series because there are multiple aspects to discuss and we need to focus on one at a time. Here is another item from the JST of Genesis 14 that I have not highlighted yet but want to discuss in this post
33 And now, Melchizedek was a priest of this order; therefore he obtained peace in Salem, and was called the Prince of peace...
36 And this Melchizedek, having thus established righteousness, was called the king of heaven by his people, or, in other words, the King of peace.
Why was Melchizedek called both king of peace and prince of peace? Alma 13 gives a possible clue
But Melchizedek having exercised mighty faith, and received the office of the high priesthood according to the of God, did preach repentance unto his people. And behold, they did repent; and Melchizedek did establish peace in the land in his days; therefore he was called the prince of peace, for he was the king of Salem; and he did reign under his father. (Alma 13:18)
He literally was the king of peace since he was the king of a city named Salem (meaning peace in Hebrew and which most scholars agree was Jerusalem). But since he simultaneously was a king and reigned under his father, he was both king and prince. We know little about Melchizedek but absolutely nothing about his father. We can reasonably assume that he was righteous based on what we know about Melchizedek and the fact that he reigned under him.
But there might be deeper underlying truths to this idea of being a prince of peace. There are three persons in the scriptures that are referred to as prince of peace. In addition to Melchizedek, only Abraham and Jesus Christ get this title. Interestingly, the father/son or king/prince duality is a recurring theme. Notice for instance the extensive use of "father/fathers" in the beginning of the Book of Abraham where Abraham seeks to become a prince of peace
1 In the land of the , at the residence of my fathers, I, , saw that it was needful for me to obtain another place of ;
2 And, finding there was greater and peace and rest for me, I sought for the blessings of the fathers, and the right whereunto I should be ordained to administer the same; having been myself a follower of , desiring also to be one who possessed great , and to be a greater follower of righteousness, and to possess a greater knowledge, and to be a father of many , a prince of peace, and to receive instructions, and to keep the commandments of God, I became a rightful heir, a , holding the right belonging to the fathers.
3 It was upon me from the fathers; it came down from the fathers, from the beginning of time, yea, even from the beginning, or before the foundation of the earth, down to the present time, even the right of the , or the first man, who is , or first father, through the fathers unto me.
4 I sought for mine unto the Priesthood according to the appointment of God unto the concerning the seed.
To become a follower of righteousness and prince of peace, Abraham needed to be appointed unto the Priesthood. This priesthood was a patriarchal order, transmitted from father to son, creating kings and princes, like Melchizedek who became the archetype of a holder of this priesthood. In the original language, Abraham, means "father of a multitude". The wordplay is evident: "In the land of the Chaldeans, at the residence of my fathers, I, Father of a Multitude...sought for the blessings of the fathers".
The only other passage of scripture containing the title "prince of peace" is Isaiah 9:6
For unto us a is , unto us a is given: and the shall be upon his shoulder: and his name shall be called Wonderful, , The , The Father, The Prince of .
Again we see the pattern of father and son (implied by prince). We know that Jesus Christ is both the father (in more than one sense) and the son. Some people trip over the oddity of that passage to our modern ears, but I find it beautiful
1 And now Abinadi said unto them: I would that ye should understand that himself shall down among the children of men, and shall his people.
2 And because he in he shall be called the , and having subjected the flesh to the of the , being the Father and the Son—
3 The Father, he was by the power of God; and the Son, because of the flesh; thus becoming the Father and Son—4 And they are , yea, the very of heaven and of earth. (Mosiah 15)
What we have seen so far is that there are three persons with the title, Prince of Peace in the scriptures: Melchizedek, Abraham and Jesus Christ. In each case, there is a father-son theme. I think it has much to do with the priesthood. The Melchizedek Priesthood is not dependent on a tribe like the Levitical Priesthood. It's a pattern of Father-Son family priesthood. Paul spends much of his letter to the Hebrews that this is the priesthood that Jesus came to restore
5 So also Christ glorified not himself to be made an high priest; but he that said unto him, Thou art my , to day have I begotten thee.
6 As he saith also in another place, Thou art a after the order of .
There is no coincidence that Abraham, the father who sought for the blessings of the fathers, is mentioned so much in D&C 132. We get too hung up on plural marriage sometimes that we miss the beautiful truths about the priesthood and the everlasting covenant.
28 I am the Lord thy God, and will give unto thee the of my Holy Priesthood, as was ordained by me and my Father before the world was.
29 received all things, whatsoever he received, by revelation and commandment, by my word, saith the Lord, and hath entered into his exaltation and sitteth upon his throne.
30 received promises concerning his seed, and of the fruit of his loins—from whose ye are, namely, my servant Joseph—which were to continue so long as they were in the world; and as touching Abraham and his seed, out of the world they should continue; both in the world and out of the world should they continue as innumerable as the ; or, if ye were to count the sand upon the seashore ye could not number them.
31 This promise is yours also, because ye are of , and the promise was made unto Abraham; and by this law is the continuation of the works of my Father, wherein he glorifieth himself.
32 Go ye, therefore, and do the of Abraham; enter ye into my law and ye shall be saved.
As we enter into the law of the Melchizedek Priesthood, we like Joseph Smith, are the seed of Abraham and the same promises apply to us. That is, as Abraham's seed, our seed will also perpetuate into the eternities. This is how the priesthood and the covenant are preserved, from father to son becoming kings and princes. It is perhaps confusing then that Paul states:
father, without mother, without descent, having neither of days, nor end of life; but made like unto the Son of God; abideth a continually. (Hebrews 7:3)
From the context, it seems like Paul describes Melchizedek here. But Joseph Smith clarifies and explains that this does not apply to the person, Melchizedek, but rather his priesthood.
For this Melchizedek was ordained a priest after the order of the Son of God, which order was without father, without mother, without descent, having neither beginning of days, nor end of life. And all those who are ordained unto this priesthood are made like unto the Son of God, abiding a priest continually. (JST Hebrews 7:3)
Early Christian extra-Biblical sources show that there was a great deal of confusion back then as well. Some considered Melchizedek as a divine figure and perhaps even the pre-mortal Christ himself. Others considered him just a mortal man, although a righteous high priest. I think the confusion comes from the fact that Melchizedek became the archetype of a priesthood holder after the order of the Son of God. Epitomizing this order, the man and the priesthood got confused as the tradition was passed down, scriptures were lost and perhaps deliberately changed. This is just my theory anyway.
The point is that the priesthood itself is eternal, without father and descent, while those who enter into this order become part of an eternal chain of father and descent. They are the seed of Father Abraham (who sought the blessings of his fathers) and receive the promise that their seed shall continue "out of the world". They become princes of peace and kings of righteousness, like Abraham and Melchizedek, receiving all these promises that are too great to fully comprehend.
Let me just add as a final note that I think princess, queen and priestess applies just as much. Despite the technicalities of the patriarchal order where men are ordained at least here on earth, the promises and blessings apply in equal measure and women obviously have a sacred role in the "continuation of the seeds for ever and ever" (D&C 132:19).