If you quoted a price including labour and materials no you do not. If you bought them on his behalf you do. If you quoted using a specific product and there is doubt you provided the item as specified then you should show him the receipt.
If there has been a price quoted including material and labor, no there does not have to be proof of what was spent for material, if there was a agreement that the worker gets material and bring you a receipt than yes, so you really have to know business and have this all sorted out on the front end you don't make decisions in the middle of the stream...the best to you
I am pretty sure they don't Have to but it would be a really good idea to do so. One thing to show what all has been done, and to show that you are being honest with someone.
Yes, if you are not supplied with materials costs, you are not legally liable for a bill, unless it was a flat price you agreed on.