What do you do if your son damages a vase in a store in a foreign country and doesn't pay for it, and do you pay the amount to the store or to one of the mosques?

If a child destroys something, he is liable for it from his own wealth. If he has no wealth, then one waits until his financial situation becomes easy. His guardian is not obligated to compensate, unless he volunteers to do so. If you wish to volunteer on behalf of your son, then you must pay the price of the destroyed item to the shop owner or seek his forgiveness. Donating the price to the mosque is not sufficient.