1)
Why does it say "Ki Fadah
1.
Radak (9): Via this, the Goyim will know that they did not exile Yisrael with their strength. Refer to 31:9:2:1.
2)
Is there a difference between Padah and Ga'al?
1.
Malbim: Padah was from the afflictions, amidst mercy. Go'el is due to His closeness [to Yisrael]. Amidst mercy, one will give money to redeem. One will risk his life only for a relative!