Is it permissible for a worker to take money he found in a house he is renovating, knowing that the house belongs to a non-Muslim and the money has been buried for about 12 years?

It is not permissible for the worker to take the money he found in the house; rather, it belongs to the homeowner, whether Muslim or non-Muslim. Jurists have stipulated that whatever is found on owned land belongs to the landowner. If the current possessor does not claim it, then it belongs to the one who had possession before him, and so on.