How did Hashem resolve Moshe's first question ("Who am I ... ?")
Rashi and Rashbam: By pointing out to him that a. since he was Hashem's Shali'ach, Hashem would accompany him when he went to Pharaoh 1 and no harm would befall him, and b. the burning bush was a sign that he was Hashem's Shali'ach and will succeed and not be harmed, just like it is not consumed.
Ramban: 'Do not fear Pharaoh, because I am with you!'
Seforno: Hashem informed him that a. He would be with him, and that would be a sign, in that all his commands would take effect, because everybody would thereby acknowledge that Hashem had sent him and would hold him and his words in the highest esteem. 2
Rashi (verse 11) said that Moshe's second question was what is Yisrael's merit to leave Egypt? How did Hashem answer this?
Rashi #1: At the end of three months after leaving Egypt, they would receive the Torah on the very mountain upon which he was standing.
Rashi #2: The fact that Moshe would succeed in his mission was a sign that Yisrael would serve Hashem (receive the Torah) on that mountain; and that was the merit that would stand for Yisrael. 1
Ramban, Da'as Zekenim: 'And the sign for the people to know that I sent you to them is, that after leaving Egypt, you will serve Hashem on this mountain.' From then on, they will undertake to worship Hashem and to obey his commands and they will believe in you forever and go wherever you command them to. This is their merit.
Rashbam: Hashem instructed Moshe to tell Pharaoh that all they wanted, was to sacrifice to Hashem on that mountain 2 - a request that he could reasonably accept.
Seforno: Even though Yisrael were not worthy when they left Egypt, they were prepared to serve Hashem on the mountain.
The same concept is to be found in Yeshayah, 37:30, where the downfall of Sancheriv was a sign that, although there was a draught, Hashem would bless the Sefichim (the wild seeds [Rashi]).
Rashi writes that at the end of three months after leaving Egypt, they would receive the Torah. It was more than a year when Moshe came to Pharaoh, and less than two months after they truly left!
Moshav Zekenim (1): Kabalas ha'Torah was completed after Moshe was on Har Sinai for 40 days. This was 90 days from Yetzi'as Egypt.
Moshav Zekenim (2): Part of a month counts like a month 1 - the three months are Nisan, Iyar, Sivan.
If so, why did Rashi say 'at the end of three months? (PF)
How is 'you will serve Hashem on this mountain' a sign for Moshe to believe now?
Moshav Zekenim (1): The burning bush was a sign that Moshe will not be harmed [just like it is not consumed]. ''You will serve Hashem on this mountain' answers 'v'Chi Otzi...', i.e. what is Yisrael's merit to leave Egypt?
Moshav Zekenim (2): The signs for Moshe to believe now were the staff becoming a snake, Tzara'as of the hand, and water turning to blood. ''You will serve Hashem on this mountain' is the purpose of the mission.
Moshav Zekenim citing the Rambam: The wonders Moshe did in front of Bnei Yisrael caused them to believe in him temporarily. At Matan Torah, they will acquire permanent trust in him.
רש"י: וזה המראה...לך האות כי אנכי שלחתיך: למה נזקק משה לאות על כך?
גור אריה: משה ידע שה' שולח אותו, אבל ה' גילה לו כאן שכל השליחות היא "לא משלך אלא משלי" ולכן יהיה ה' עמו.