What exactly, is the "Yad ha'Gedolah"?
Rashi: It is synonymous with the great might with which Hashem dealt with the Egyptians.
Ramban #1 (citing Targum Onkelos): It refers to the Might of Hashem's Right Hand (the Midas ha'Din 1 ), with which He struck the Egyptians.
Ramban #2 (citing the Ibn Ezra): Yad ha'Gedolah is another way of saying the great plague (stroke). 2
Ramban #3 (according to Kabalah): It is written with reference to Hashem's Midas ha'Din. 3
Targum Yonasan: It refers to the Mighty Hand of Hashem with which He performed miracles in Egypt.
Lev Eliyahu (p. 122) It is His supernatural Hashgachah.
Whilst it was with the Midas Chesed of the same Hand that He saved Yisrael (See Rav Chavel's notes).
Similar to the Pasuk (9:3) "Hinei Yad Hashem Hoyah b'Miknecha" (Ramban).
What are the ramifications of the fact that they believed in Hashem?
Rashbam: They now knew that they would not die of starvation in the desert.
Why does it say that they feared Hashem before they believed in Him?
Lev Eliyahu (p. 122) To reach fear, they needed to see His supernatural Hashgachah. After this, they reached Emunah Chushis, i.e. like one who is holding his father's hand. This is a higher level than fear.