The רמב״ן, רד״ק  and שער בת רבים explain that the reason why פרעה was happy when he saw יוסף’s family was because now he saw that יוסף came from a חשוב family and he wasn’t worried that maybe he had a person from a family of slaves running Egypt.  The ספורנו explains that פרעה  and his servants were happy when יוסף’s family came because then they knew that יוסף would stay in מצרים.

The פסוק  says ״ויצא האחד מאץ ואמר אך טרף טרף״. Rav Moshe Shternbach darshins that it means that when the אחד, the אחדות, leaves us that is when we get destroyed.   Conversely, Rav Yechezkel M’klosmir says that יוסף and בנימין crying over the other person’s צרה (the destruction of the בית המקדש and משכן שילה) teaches us that the way to rebuild the בית המקדש is when you care for your fellow Jew more than yourself because מעשה אבות סימן לבנים.

Rav Moshe Shternbach explains that יעקב said שמע when he saw יוסף because he now realized that everything that happened was all orchestrated out of the mercy of ה׳.   Rav Kalish explained a little differently. He said that the שם ה׳ is מדת הרחמים and the name אלקים is מדת הדין. So in שמע we first say both of those and then we say ה׳ אחד, meaning that יעקב was saying that at first he thought there were two separate מידות of ה׳ and then he realized that everything is really רחמים.   The מהר״ל says that when a צדיק sees a time of שמחה he adds עול מלכות שמים and that is why יעקב was saying קריאת שמע. Rav Binyomin Jacobs said that יוסף didn’t say שמע because he had to be מקיים the מצוה of כיבוד אב ואם.

The  גר״א says that because יעקב told פרעה that they are only coming to “dwell” in מצרים then that enabled us to get out of מצרים, and we see this in the הגדה to teach us that it was one of the reasons the גאולה could come.

Rav Moshe says that the פסוק tells us that יעקב lived in מצרים and in  גושןeven though we know that גושן is in מצרים to emphasize that even though he lived in an all-Jewish place, like גושן, he still realized that he was in גלות.   Also, Rav Moshe said that יעקב sent יהודה  to start a ישיבה in מצרים to remind the Jews that they need to live like a Jew no matter where they are.

Harav Gamliel Rabinovich says that יוסף told the brothers to tell פרעה that they are shepherds because when you tell the יצר הרע that you are lowly it won’t bother you.

Rav Binyomin jacobs explains that here reason why יוסף told יעקב that he was ”״אדון בכל מצרים” was because he added the words ״שמני ה׳״ that ה׳ put him there, so he won’t run after power and get influenced because he knows it is all from ה׳.