Why did the Torah interrupt the Parshah of Yosef with that of Yehudah?
Refer to 38:1:1.
Why did the descent of Bnei Yisrael to Mitzrayim have to come about through the sale of Yosef?
Maharal (Gevuros Hashem, beg. Ch. 11): Had Yaakov been drawn towards Mitzrayim for less of a reason (e.g. the famine), Yaakov would have sensed subconsciously that they would be enslaved there, and he would have avoided going. Now that he was descending to be reunited with Yosef, he ignored all other factors and went down willingly. 1
Maharal: The Midrash Rabah (86) compares this to a cow unwilling to be led to its place of slaughter, for it can sense what awaits it. The butcher walks with the calf before her, and the cow has no choice but to follow.
Why did the descent of Bnei Yisrael to Mitzrayim come about through the sale of Yosef, rather than Yaakov being forced to descend by Pharaoh?
Maharal (Gevuros Hashem, beg. Ch. 11): Whereas a forced descent may have been appropriate to enforce Hashem's decree (to show Midas ha'Din); for the sake of the Tzadik, Hashem did not disgrace Yaakov in this manner.
Why did the descent of Bnei Yisrael to Mitzrayim come about through the sale of Yosef? Why didn't Hashem just give Pharaoh the idea to invite Yaakov and his family, for their own benefit?
Maharal (Gevuros Hashem, beg. Ch. 11): Had that been the case, it would not have been evident that these events were from Hashem. The exile to Egypt came about in this miraculous way, to show that Hashem decrees 1 and fulfills.
Hashem decreed and informed Avraham of this exile and slavery, at the Bris Bein ha'Besarim (Bereishis 15:13).
Why did the descent of Bnei Yisrael to Mitzrayim come about through Yosef in particular, and not through one of the other tribes?
Maharal (Gevuros Hashem, beg. Ch. 11): The Egyptians were basely materialistic (Chomer); and were steeped in sexual immorality. Yosef, in contrast, was holy, separated from any such misconduct (as we see later in this Perek). Just as Tzurah by definition rules over the Chomer, 1 it was fitting that Yosef rule over Mitzrayim.
In the terminology of Maharal, "Chomer" is raw material or potential, while "Tzurah" (lit. form) is the actualization and fulfillment of that potential. (To illustrate, in a knife, the iron is the Chomer, and the sharp edge is the Tzurah.) A materialistic person has no particular goal that guides his conduct; he is driven only by opportunity and lust. When a person of stature (Tzurah) takes charge, he gives his subjects purpose and helps them to actualize their potential. This is what Yosef did for Mitzrayim. (EK)
Why didn't Hashem bring about Yosef's ascent to the throne, immediately upon his arrival in Mitzrayim?
Maharal (Gevuros Hashem, beg. Ch. 11): In a person's youth, his Chomer overpowers the Tzurah (i.e. he is drawn to the physical over the intellectual, and acts in a juvenile manner); until he matures. The same was true for Yosef; he was 17 years old when sold, and he was raised to the throne only at age 30.
Why does the Pasuk refer to Potifar as 'Seris Pharaoh'?
Targum Onkelos and Targum Yonasan #1: It means that he was an important officer of Pharaoh. 1
Targum Yonasan #2: The word 'Saris' can also mean a eunuch, which is what Potifar became. When he bought Yosef for immoral purposes, Hashem caused his sexual organs to dry up and he became impotent. 2
What exactly, was Potifar's position?
Refer to 37:36:3.
This verse states that Potifar purchased Yosef "from the hands of the Yishma'elim." (The Yishma'elim also appeared in 37:28). But verse 37:36 tells us that it was the Medanites who sold Yosef to Potifar!
Ramban and Seforno: Refer to 37:28:1:2.
R. Chaim Paltiel: When the Yishma'elim offered to sell the good-looking Yosef to Potifar, he suspected them of having stolen him, 1 and that the owners would eventually come and re-claim him - until the Medanim arrived and guaranteed that Yosef was not stolen and that the sale was genuine.
Moshav Zekenim (to 37:25): The Medanim do not normally sell people. When they wanted to sell Yosef, the Egyptians suspected that they stole him, until the Yishma'elim testified (that the Medanim bought him). 2
Rashbam: Refer to 37:36:1:2.
Gur Aryeh #1 (to 37:28): The Midyanim dressed like Yishma'elim, and Potifar addressed them as such (just as the brothers had also addressed them as Yishma'elim). But in fact, they were Midyanim. Refer to 37:28:1.01:2.
Gur Aryeh #2 (to 37:28): The caravan was primarily Yishma'elim, but Yosef was sold to, and later purchased from, the Midyanite merchants among them. 3 Refer to 37:28:1.01:3.
Riva (to Bereishis 37:36): Potifar suspected them, for it was uncommon for black people to sell white people. Rosh (to Bereishis 37:28) - It was common for white people to sell blacks, but not vice-versa. Medanim and Midyanim are the same; they were middlemen in the sale, and the Yishma'elim hired them to come to Egypt to testify about it. R. Tam - Medanim are a different nation. They did not have money to pay for him, so they left him in the Yishma'elim's hand until they sold him.
Gur Aryeh (ibid.): According to the Midrash, Yosef was bought and sold multiple times. Refer to 37:28:1.03. (For the symbolism behind these multiple stages, refer to 37:28:1.03:3 and the notes there.) Nevertheless, our verse tells us that Potifar purchased Yosef from the Yishma'elim, in the sense that they comprised most of the caravan. Alternatively, Yosef had not been in anyone else's hands in the practical sense (i.e. during the trip he was sold on paper).
Having said, "v'Yosef Hurad Mitzraymah," why does the Torah see fit to repeat "Asher Horiduhu Shamah"?
Oznayim la'Torah: Following the principle 'Ein Mi'ut Achar Mi'ut Ela l'Rabos' (two preclusions come to include), we can explain that this was not a Yeridah, but an Aliyah, since ultimately, it led to Yosef's rise to greatness.
Why does the Torah use the passive form "Hurad" (Yosef was taken down)?
Da'as Zekenim, Hadar Zekenim: This shows that it was due to Hashem's decree [that Bnei Yisrael would descend to Egypt].
Why did the Torah need to repeat the fact that Potifar bought Yosef from the Yishma'elim?
Ha'amek Davar: The custom was, if a slave owner could not wait for a buyer, the Dimusiya of the country bought him and later sold him. Potifar was appointed to do this, so he could not buy him himself (just like a Gabai Tzedakah may not buy [food or other matters of] Tzedakah, due to suspicion 1 [that they pay less than its true value]). Potifar covered up that the Dimusiya already bought Yosef, and arranged that the Yishma'elim now sell him, so he himself could buy him. It is not because Potifar was a Kena'ani that he did so; he was Ish Mitzri. (Through Hashgachah, he strove to buy Yosef.)
Bava Basra 8b.
QUESTIONS ON RASHI
Rashi writes: "'Yosef was brought down, etc.' - [The Torah] returns to its previous topic." What is Rashi coming to explain?
Gur Aryeh: We already learned that Yosef was sold to Egypt, in verse 37:36. The Torah repeats this here, in order to resume the story that had been interrupted.
Rashi writes: "... And furthermore, [the Torah wrote the story of Tamar here] to place the deed of Potifar's wife adjacent to that of Tamar...." Why does Rashi need to give both reasons?
Gur Aryeh: The story of Yehudah and Tamar (Bereishis 38) is comprised of two sections. The first section (38:1-11) is inserted here to teach the reason that Yehudah was demoted from among his brothers - because of his role in the sale of Yosef. 1 The Torah continues with the story of Tamar (38:12-30), to compare it with the following story of Potifar's wife (in that both intended l'Shem Shamayim).
As Rashi (to 38:1) wrote above as well.