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).
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].