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.

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.