If an interception occurs on an illegal forward pass, is there a change of possession or does the offense retain the ball with a five yard penalty and loss of down?

Both are possible. Both teams can catch and advance an illegal forward pass. If an illegal forward pass hits the ground it is incomplete. The defense can decline the penalty and keep the ball or they can accept it and make A take the 5 yards back from the spot of the foul and have a loss of down.

I'll give you three guesses as to what the defense does 999 times out of 1000.