If god did answer your prayer here, he implanted the thought into your friend's head to buy the food. Therefore, your friend's free will, free mind was indeed tampered with.
No, your friend still made the choice whether or not to put the groceries on your door. The friend could have decided that you were a no good bum and you need to help out your own family. Because your friend loves you, it is unlikely that they would decide that. They would, instead, decide to follow the Lord's suggestion.
R