Who was Malki-Tzedek, and where was Shalem?
Ramban asks: If Malki-Tzedek was alias Shem, what was he doing in Yerushalayim (which was situated in the territory belonging to Cana'an)?
Ramban: He left his hometown to go and live in Yerushalayim to serve Hashem there, and they appointed him Kohen.
Ramban asks: "Shalem" and "Tzedek" are synonyms with Yerushalayim, [as we find in Tehilim 76:3 and Yeshayah 1:21, respectively], and kings of Yerushalayim were called "Tzedek" (such as here, and Adoni-Tzedek in Yehoshua 10:1). But of what significance was Yerushalayim to the nations of the world before David made it the capital of Yisrael?
Ramban: The nations were aware, from time immemorial, that Yerushalayim was the epicenter of the universe, or that Yerushalayim here corresponded to Yerushalayim in Heaven, where the Shechinah, which is called Tzedek, is to be found. 1
See also the Midrash cited by the Ramban.
What point was Malki-Tzedek making when he brought bread and wine to the returning soldiers?
Rashi #1: Besides performing an act of kindness on behalf of the battle-weary soldiers, he was demonstrating that he did not hold it against Avraham (his great-great... grandson) for killing his descendants 1 (e.g. Kedorla'omer, king of Eilam 2 ).
Rashi #2: He was hinting at the flour-offerings and the wine libations that their joint descendants would later bring in that very same location. 3
What is the significance of the fact that Malki-Tzedek was a Kohen?
Rashi (to 14:20): That explains why Avraham gave him Ma'aser. 1
Seforno: Since he was a Kohen, it was befitting for him to bless Avraham (14:19).
Ramban: Avraham only gave him Ma'aser 2 in honor of "the High G-d (Hashem)" to whom Malki-Tzedek served as Kohen.
Why does the Pasuk refer to Haahem here as "Kel Elyon"?
Ramban: Whereas all the nations had priests who worshipped the angels (who are called "Eilim" - as in "Mi Chamocha ba'Elim Hashem?", the Pasuk informs us here that Malki-Tzedek worshipped "Keil Elyon" (Haahem, Master of the Eilim).
What hint does this Parshah contain to the future history of Am Yisrael ("Ma'aseh Avos Siman la'Banim")?
Ramban: (a) This was destined to be the location of the House of G-d; (b) There his descendants would eventually bring their T'rumos and Ma'asros 1 , and (c) there they would bless Hashem.
Why does the Torah interrupt between "va'Yeitzei Melech Sedom" (14:17) and "va'Yomer Melech S'dom" (14:21) with the episode concerning Malki-Tzedek?
Rashbam and Riva: To explain why, when Avraham referred to "what the young men ate" (14:24), and not "what we ate," he was not lying, since he personally ate only what Malki-Tzedek gave him (and not from the spoils). 1
Ramban (to 14:20): Because it was only after the king of S'dom saw Avraham's benevolence (when he gave one tenth of all that he had to Shem), that he asked Avraham to return the captives.
Moshav Zekenim says similarly
Why does it say, "He (Shem) is a Kohen"?
QUESTIONS ON RASHI
Rashi writes: "Malki-Tzedek - According to the homiletic Midrash, this was Shem ben Noach." How can this be shown?
Gur Aryeh #1: The verse concludes, "He was a Kohen to Kel Elyon." Noach had become a Ba'al Mum at the end of the Flood (Rashi to 7:23), 1 and was disqualified to serve as Kohen; the sacrifices after the Flood (8:20) must have been offered by Shem, who was the most worthy of Noach's children. 2 Shem then continued to serve as Kohen for the rest of his life.
Gur Aryeh #2: "Shalem" is Yerushalayim, which was part of the territory allotted to Shem; 3 certainly he would be its king, and none other.
Rashi writes: "Malki-Tzedek... was Shem ben Noach." He could have been called Melech-Tzedek; what is the symbolism of the added Yud?
Gur Aryeh: The Yud represents the ten generations that Shem reigned, including that of Avraham. 1
What does this teach us? See Maharal (Derech Chayim 5:3, p. 221), who teaches that the "ten generations from Noach to Avraham" did not include Avraham himself, for Avraham was distinct from all who came before him (refer to 11:32:2.2:2). Perhaps this verse teaches that Shem himself was in the same league as Avraham, for both were Kohanim. Even so, Shem did not reach Avraham's level; Shem did not pass along his priesthood to his descendants. (EK)
Rashi writes: "Shem alluded to the Menachos and Nesachim." Why did he not offer Avraham meat, to allude to the [animal] Korbanos?
Gur Aryeh: That would appear as if designating a Korban and then eating it; whereas bread and wine was the standard fare given to weary soldiers.