If you cast a spell for an alternative cost of {0}, you can't pay any other alternative costs. You can, however, pay additional costs, such as kicker. If the card has any mandatory additional costs, you must pay those.

You pay all costs and follow all timing rules for cards played with the permission granted by Charred Foyer's ability. For example, if the exiled card is a land card, you may play it only during your main phase while the stack is empty.