Ask the church for one--they surely have a Tax ID. In order to get the childcare credit you must enter a Tax ID for the childcare provider.
Yes you need to ask the church for their tax ID. Better yet, they should give you a receipt showing paid expense, address and tax ID.
Yes, you can claim the childcare expenses paid to a church preschool.
Select Other >> Tax-exempt organization when you enter information about your care provider.