They are required to give you form W-10 with their tax ID number. There are no exceptions.
They are not required to provide you with a year-end statement, whether or not you pay on time. Some care centers might for your convenience, but you are required to keep your own accurate records of what you paid. (Canceled checks, receipts, etc.) You also can not claim any expense for a tax credit that you have not actually paid in 2015.
