Why did Moshe refer to Hashem as 'Elokei ha'Ivrim'?
Ramban: After Pharaoh informed Moshe that he does not believe in the Name Havayah, Moshe told him that Elokei ha'Ivrim 1 had instructed them to sacrifice to Him.
Why did Moshe say to Pharaoh "Pen Yifga'einu and not 'Pen Yifga'echa'?
Rashi: Since the word refers to the death of the person concerned, it would not have been respectful to say it directly on Pharaoh.
Ramban #2: Hashem ordered Yisrael to bring sacrifices to Him because the Midas ha'Din was stacked against them and Korbanos have the power to protect against the Midas ha'Din. 3
See Ramban's refutation of this explanation.
Moshe was actually responding to both of Pharaoh's previous statements (Refer to 5:2:2:1); a. 'Hashem' is the G-d of the Ivrim, who follow the teachings of Eiver (Shem's grandson); and b. Pharaoh would be well-advised to obey Him ... (Seforno).
What is "v'Hu Yada" coming to teach us?
Rashi (Shabbos, 2b) and Rashbam: It teaches us that after forgetting the Tum'ah (or Kodesh or Mikdash), he remembers it. 1
Why does repeat the phrase ve'Ne'elam mimenu"?
To teach us that he initially knew that he was Tamei (and that he was eating Kodesh or entering the Mikdash) and then forgot. 1
Rashi #2 (Shabbos, 2b): This time it comes to include one who forgot that he is in the Beis-ha'Mikdash or that what he is eating is Kodesh.
Why did they say that they must go away in order to offer to Hashem?
Da'as Zekenim, Hadar Zekenim, Riva: If we would sacrifice the deity of Egypt [in front of them, they would stone us].