What is the significance of Hagar's calling out the Name of Hashem?
Rashi: She acknowledged that Hashem takes the side of those who are put to shame, as He took her side.
Targum Yonasan: She thanked Hashem for having answered her prayers.
Seforno: Calling out the Name of Hashem is an expression of Tefilah - since praising Hashem always precedes prayers. 1
As the Gemara states in Berachos 32a.
Why did she refer to Hashem as "Keil Ro'i"?
Rashi: Because Hashem sees - He takes the part of those who are shamed.
Seforno: Because Hashem is the G-d of vision - He sees everything 1 wherever it may occur - even not in Avraham's house.
Targum Yonasan: Hashem sees, but cannot be seen.
Which is also how Targum Onkelus translates it.
Why was Hagar so surprised to see angels?
Targum Yonasan: She was not surprised. What she was saying 3 was although Hashem cannot be seen, His Shechinah appeared to her (via an angel), after having seen angels earlier.
Rashi: As is evident from the fact that she displayed no fear upon seeing four angels, one after the other (as opposed to Mano'ach, Shimshon's father, who was afraid that he would die, after seeing only one. However, the Malbim (Shoftim 6:22) explains that Mano'ach and Gid'on feared only after seeing the angel remove his physical form; Hagar did not see this.).
Gur Aryeh: Rashi explains the Pasuk as follows: "You, Hashem, see the insult of the downtrodden! Not only in the house of Avraham did I see angels [that appeared due to his merit], but even here in the desert; for You saw [my] shame."
What did Hagar mean by, "Acharei Ro'i"?
Riva: When the angel turned around, she did not see anything. She deduced that he was an angel.