Why did Hashem command Yisrael to go back towards Egypt?
Rashi: To trick Pharaoh into believing that they were lost - to encourage him to chase after them. 1
What is the significance of Pi ha'Cshiros?
What is the significance of Ba'al Tzefon?
Rashi and Targum Yonasan: It was the only idol to survive Makas Bechoros. Hashem did so in order to fool Pharaoh into believing that it was all-powerful 1 and able to stand up to Hashem (Kevayachol). 2
See Sifsei Chachamim.
Moreover, it had succeeded in trapping Yisrael beside the Yam-Suf, for his army to attack - another means employed by Hashem to lure Pharaoh and his army to the Yam-Suf (Refer to 14:2:1:1*), as the Pasuk writes in Iyov (12:23) "He tricks the nations and destroys them" (Rashi, citing the Mechilta). The Seforno (in Pasuk 5) adds that they erred in not first consulting Ba'al Tzefon before sending Yisrael away - and Pharaoh and the Egyptian army now came to bow down to it and to praise it (Targum Yonasan [Refer also to 14:10:13).
Why does it say "Lifnei Ba'al Tzefon"? One may not mention an idol to designate a place!
Da'as Zekenim: It is forbidden for people but permitted for Hashem, just like He judges on Shabbos, Rosh Hashanah and Yom Kipur, which is forbidden for people. 1
Sanhedrin 63b: Any idolatry mentioned in the Torah, one may mention its name. 2
Rashi (Rosh Hashanah Sof 30a): People may not build the Mikdash on Yom Tov or at night, but Shamayim may. Hadar Zekenim left the question difficult. He holds that Hashem observes the entire Torah; Sanhedrin 39a implies so. (PF)
Hadar Zekenim left the question difficult. He must hold that since the Torah was not yet given, this Heter did not apply. (PF)