Item 1 - Delay to flight to London - hotel costs and EC261 compensation are due to be paid by the operating carrier

AA is not liable for the hotel, breakfast, taxi or bus - that is the responsibility of the airline that caused the issue (I assume it was BA)

With your AA ticket - what was the cancellation penalty and change fees on the ticket? that you were told to purchase a new ticket, it would suggest that you had a non changeable ticket.

It is true that another department handles refunds - was your ticket refundable? if not then you are unlikely to receive a refund.

What exactly was the ticket that you had?