Why does the Torah use the double expression "Hashbe'a Hishbi'a"?
Rashi: Because he made his sons swear that they would make their sons swear ... until they left Egypt.
Why did Yosef not make his sons swear that they would take him out of Egypt, like his father did to him?
Rashi: Because, unlike himself (who had the authority to take his father out of Egypt and bury him in Eretz Kena'an), Yosef knew that the Egyptians would never allow his sons to take his body from Egypt.
Hadar Zekenim: Yakov made Yosef swear, for Yosef had more authority to take him than his brothers did. Yosef knew that his sons had no more authority than others, so he made all [his brothers] swear.
Hadar Zekenim, from Bereishis Rabah 85:3: He told his brothers 'you stole me from Shechem. 1 Return me to Shechem!'
Why did specifically Moshe take Yosef's bones out of Egypt?
Seforno: Because he was the leader of that generation, and the obligations pertaining to the generation falls upon the leader to fulfill.
Moshav Zekenim: He wanted to show that Yosef pardoned Moshe's grandfather Levi. 2
What are the connotations of the word "Itchem" which Yosef said whilst speaking to his brothers?
Rashi: He hinted to his brothers 1 that their bones too, would be taken out of Egypt by their respective children.
See Sifsei Chachamim.
Why is this written here on the second day [after leaving Egypt]? Did Moshe not take the bones on the first day?!
Moshav Zekenim: Surely he took the bones on the first day, but they were mixed with the bones of his brothers. After they came to Sukos and were more settled, he separated Yosef's bones.
Why does it say that Moshe took Yosef's bones? In Yehoshua (24:32), it says that Bnei Yisrael took them!
Moshav Zekenim: Moshe made Bnei Yisrael zealous to take them, therefore it is attributed to him [in the Torah].
Moshav Zekenim citing R. Moshe: Moshe took them, but he could not enter Eretz Yisrael, so Bnei Yisrael buried them in Shechem. Because they finished the Mitzvah, [in Sefer Yehoshua] it is attributed to them (Sotah 13b).