We have a borrower who did not have adequate credit for approval, so her father agreed to jointly apply for the loan with her. Is it necessary to provide an AAN to the borrower for the first application (without the father)?

If the loan is made, it would be an accepted counteroffer, wouldn't it?

This is where I get confused. If a counteroffer, would an official written counteroffer have had to been provided under Reg B, or could it have been strictly verbal and the fact that a counteroffer was made simply be noted in the file?

There is no requirement that the counter-offer be reduced to writing.