Why did they 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 unto Him.
Oznayim la'Torah: Refer to 5:1:2:1. They thought that Pharaoh's insulting reply was due to the fact that they changed from Hashem's wording. 2 So they changed back to it.
Ramban: The equivalent of Kel Shakai (as Hashem was known to the Avos), whom Pharaoh (who was a wise man) did acknowledge - See Bereishis 41:39), ordered them to bring sacrifices to Him. Indeed, Moshe had already mentioned this Name to Pharaoh. See above, Shemos 3:18.
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 #1 (citing the Ibn Ezra) 1 and Seforno: Moshe was warning Pharaoh that, if he refuses to let Yisrael go and worship Hashem, Hashem would punish both him, all Egypt, and Yisrael. 2
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.
Seforno: 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 Ever (Shem's grandson); and b. Pharaoh would be well-advised to obey Him ....
Ramban: Like we find by Bil'am and Balak (See Bamidbar 23:4).
What is the significance of a three-day's distance?
Maharal (Derech Chayim p. 187, to Avos 4:14): When travelling three days away, one is still connected to one's previous [environment]. In requesting a three-day's journey, Bnei Yisrael implied that they would not go so far [as to disconnect from Egypt] completely. 1
Maharal: Similarly, in the desert, the Aron would travel a three day's journey ahead of Bnei Yisrael (Bamidbar 10:33), and no further. Also see Maharal (Ohr Chadash p. 157, to Esther 4:16) regarding the number 3; and also refer to 2:23:3.07. In the introduction to Ohr Chadash (p. 57), however, Maharal writes that only something less than three remains attached, e.g., the Halacha of Lavud. (EK)
Why did they say that they must go away in order to offer to Hashem?