Who were the Medanim?
Rashi (to Bamidbar 31:6, citing Sotah 43a): The Medanim are synonymous with the Midyanim, 1 and they resided in their land.
Rashbam: Medan, Midyan and Yishma'el were (paternal) brothers. 2 According to the simple meaning, Medan and Yishma'el were one and the same, which is why it says below (Bereishis 39:1) that the Yishma'elim brought him to Egypt and sold him there.
Bechor Shor (to 37:28): Medan, Midyan and Yishma'el are all the same, 3 just like Yehudim, Ivrim, Yisraelim and Yeshurun all refer to the same nation. The name is based on what they were carrying.
Malbim: They had pulled Yosef from the pit and sold him to the Yishma'elim, thus causing that he be sold to Egypt.
Rashi (loc. cit.): This explains why Pinchas went to fight against Midyan - to avenge the sale of his maternal ancestor, Yosef, whom they sold to Egypt. (Medan and Midyan were different sons of Keturah (Bereishis 25:2)! Perhaps he holds that Medanim are not a different nation because the Torah did not list any sons of Medan - PF.)
See Bereishis 25:2.
Riva: They are called Yishma'elim since they lived in Yishma'el's land.
If this verse tells us that the Medanim sold Yosef to Mitzrayim, why does verse 39:1 say that it was the Yishma'elim?
Gur Aryeh (to 37:28): Refer to 37:28:1.01:2, 37:28:1.01:3, and 37:28:1.03:2.
Why does the Pasuk refer to Potifar as "Seris Pharaoh"?
Ramban and Targum Yonasan #2: Refer to 39:1:2:2.
Gur Aryeh (to 39:6): It cannot mean castrated, since Potifar did have relations with his wife, as Rashi explains in 39:6,19. Rather, it means servant or official, as Targum translates.
What exactly was Potifar's position?
Rashi: Chief slaughterer of Pharaoh's animals. 1
Ramban, Hadar Zekenim, Moshav Zekenim (to Bereishis 39:1), Targum Onkelos and Targum Yonasan: Chief executioner. 2
Rashbam (to 39:1): Chief judge - to pass the death-sentence over those who were incarcerated in the royal prison.
Ha'amek Davar: The custom was, if one came to sell a slave, and it is hard to wait until he finds a buyer, the country bought him and stood him up in the market until he was sold. Potifar was appointed to this position. 3
Hadar Zekenim rejects this, for it was a To'evah to Egypt (their deity). Riva and Tosfos ha'Shalem (39:1:9) citing Moshav Zekenim say that they despised only "Ro'ei Tzon" (46:34); they worshipped only Tzon, but ate cattle. Some say that they worshipped Tzon only in Nisan, for its Mazal is a lamb. Moshav Zekenim brings Moshe's words during Makas Arov, "if we would be Zove'ach To'avas Mitzrayim in front of them, would they not stone us?!" (Shemos 8:22). This was not in Nisan, for there was a month between plagues! Perhaps he meant, 'We cannot sacrifice it even now, for they worship it in Nisan [even though in other months, also they slaughter and eat it].' This requires investigation (PF).
Ramban: Although we find the word "Tabach" in Tanach in connection with both meanings. Refer also to Bereishis 39:1.
Refer to 39:1:152:1.
Why does the Torah insert the (otherwise superfluous) words "[they sold Yosef] to Egypt"?
Gur Aryeh (to 37:28): According to an opinion in the Midrash, upon Yosef's arrival in Mitzrayim, the Medanim sold him to "Mitzrayim," i.e. to the public official 1 over that region of Egypt -- who then sold him to Potifar.
Ha'amek Davar: Potifar himself was the Egyptian official in charge of facilitating the sale of slaves. 2 Refer to 37:36:3:4.
Maharal (Gevuros Hashem Ch. 11, p. 63): A slave to the public is not completely a slave, for sometimes even a nobleman will work on behalf of the public. Only afterwards was Yosef sold to a private individual, becoming a slave in the full sense of the word.
Nevertheless, Potifar eventually managed to purchase Yosef for himself. Refer to 39:1:152:1.
QUESTIONS ON RASHI
Rashi writes: "'Sar ha'Tabachim' - [I.e. the officer in charge of] slaughter of the king's livestock." Targum, however, translates as "chief executioner." What are they disputing?
Gur Aryeh: According to Rashi, Hashem surely would not deliver Yosef into hands tainted by human blood. 1 Targum Onkelos, on the other hand, is consistent with the meaning of the term Sar Tabachim in Daniel 2:14. But in this case, Potifar would not do executions himself; he would oversee others who did the dirty work (as such, it was not disgraceful that Yosef be in his hands).
Gur Aryeh: We see that Hashem even spared Yosef the unpleasant environment of a foul-smelling Yishmaelite caravan, sending him with fragrances instead; surely He would not place Yosef in the home of a murderer!