Why did the angel move from in front of Yisrael to behind them?
Rashi and Targum Yonasan: To make a division between the Egyptian Camp and the Camp of Yisrael and to catch the arrows and slingshots that the former were shooting at Yisrael.
Ramban #1 (citing the Ibn Ezra) and Rashbam: The angel led the Cloud (mentioned later in the Pasuk) to divide between the two camps, creating darkness that prevented the Egyptians from closing in on Yisrael the entire night, whilst the Pillar of Fire lit up the night 1 for Yisrael. 2
Hadar Zekenim: This 'Mal'ach' was actually the Pillar of cloud. Later, the verse clarifies this.
Moshav Zekenim: This 'Mal'ach' was actually the Pillar of Fire. Since it has Ru'ach Chayim, it is an angel.
Rashi too, gives this explanation with regard to the Pillar of Cloud (Refer to 14:20:1:1), only he considers the angel and the Pillar of Cloud two separate entities (See Sifsei Chachamim on this Pasuk). And this is also how Targum Yonasan in this Pasuk explains it. Alternatively, "Mal'ach ha'Elokim" refers to the Beis-Din of ha'Kadosh-Baruch-Hu which dwelt in the Pillar of Fire. Refer also to 14:20:1:2.
Which was needed to lead Yisrael that night - since they had no option but to follow the pathway in the sea (Seforno).
Why does the Torah refer to it as "Mal'ach ha'Elokim" instead of the more common 'Mal'ach Hashem'?
Rashi (citing the Mechilta): This teaches us that Yisrael were standing in Din before Hashem, whether to be saved or whether to perish together with the Egyptians. 1
Besides the fact that Hashem already informed Moshe a number of times in this Parshah that He will save Yisrael (See for example Pasuk 13, 16), it is not clear why the Mechilta attributes the Midas ha'Din to Yisrael and not to Par'oh. Moreover, in Pasuk 14, Hashem said to Moshe that Hashem (Midas Rachamim) would fight on behalf of Yisrael.