I am puzzled by Melchizedek, who do you think he really was?

Hebrews doesn't actually say he was Christ incarnate. In fact, that wouldn't really make sense since Hebrews goes on to say that he is superior to the old priesthood.

Melchizedek =" my king is Sedek"

1) king of Salem and priest of the Most High God to whom Abram paid tithe after the battle he fought to free Lot; ‘the order of Melchizedek’ the order of the priesthood to which Christ belongs 18. Melchizedek—This victory conferred a public benefit on that part of the country; and Abram, on his return, was treated with high respect and consideration, particularly by the king of Sodom and Melchizedek, who seems to have been one of the few native princes, if not the only one, who knew and worshipped, "the most high God," whom Abram served. This king who was a type of the Saviour (#Heb 7:1), came to bless God for the victory which had been won, and in the name of God to bless Abram, by whose arms it had been achieved—a pious acknowledgment which we should imitate on succeeding in any lawful enterprise.

Both Rashi and Ramban state he was Shem.

Ramban has the best proof.

Malchizedek is not a name, but the title used for kings of Jerusalem, or Adonizedek.

Melech is King in Hebrew and Adoni is master.

The best explanation I can find is in the Artscroll Study Series book Bereishis.

The Man Melchizedek

To the man Melchizedek goes the honor of having his name used to identify the Holy Priesthood after the Order of the Son of God, thus enabling men to avoid the too frequent repetition of the name of Deity.

Alma, a prophet in the Book of Mormon, said that of all God’s ancient high priests “none were greater.”

So exalted and high was the position of Melchizedek in the eyes of the Lord and of his people that he stood as a prototype of the Son of God himself, the Son who was to arise “after the similitude of Melchisedec.” (Heb. 7:15).

Both bore the titles, Prince of Peace and King of Heaven–meaning King of Peace and both were joint-heirs of the Father’s kingdom. “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.” (D. & C. 84:14.)

The Apostle Paul knew much more about Melchizedek than he happened to record in his epistles. (See Heb. 11:33-34.)

There is an unsupported tradition to the effect that Melchizedek was the same person as Shem the son of Noah. That this could hardly have been the case is seen from the revelation which says: “Abraham received the priesthood from Melchizedek, who received it through the lineage of his fathers, even till Noah.”

In other words, there seem to have been at least two generations between Melchizedek and Shem.

For such an elevated prophet of God, biblical mentions of Melchizedek are too few to fully understand him and his holy calling. It was not he that was “without father, without mother, without descent, having neither beginning of days, nor end of life; . . .” but it was the holy priesthood after the Order of the Son of God that is eternal.

He was Christ. He was setting up the example of tithing. He was, is and will be the high priest of God.

In my opinion, He was and is the 2nd Person of the Trinity, God the Son. He was and is Jesus.

I'm more concerned with the real identity of Frodo the Hobbit

I believe that he was shem. Son of Noah.