1)
How would Egypt be "lMivtach Mazkir Avon"?
1.
Rashi: Hashem commanded Yisrael "Lo Sosifu Lir'osam Od" (Shemos 14:13).
2.
Radak: They removed their trust from Hashem, and trusted in Egypt.
3.
Malbim: Via turning to Egypt, they learn from their deeds and veer their hearts from Hashem.
2)
Why will they recognize "Ki Ani Hashem"?
1.
Malbim: They will recognize His Elokus, that He does to earthly kings as He desires.