Is it permissible to use a car that was mistakenly bought through an interest-based bank, knowing that I have repented and regretted that action, and I am now in a state of confusion?

Dealing with usurious banks is among the major sins. However, if it occurred out of ignorance or error, Allah has overlooked error and forgetfulness. The questioner should cancel the transaction if possible, or expedite the repayment of the principal to the bank if that suffices. If not, then he must fulfill the conditions of repentance. There is no harm in using the car purchased through a usurious transaction, because the sin of usury is related to one's liability, not to the specific asset itself.