For question one you are correct. You would not need to clear UK immigration but would simply follow the purple "Flight Connection" signs and transit via bus from T3 to T5 and then clear security there.
For question two, AA does in theory protect against this type of event but I am not sure how it would work out in practice. I can well see it happening with AA - AA flights on separate tickets but where you have BA - AA it's a lot less clear. AA's own guidance says that the carrier responsible for the misconnect is responsible for getting you to your final destination, and so that would be BA. However, from BA's perspective their responsibility is to get you to LHR and no further. AA may treat you sympathetically but you may end up having to buy a new ticket from LHR - PHL.