BA has a policy prohibiting through check of bags on 2 separate tickets, with one exception (luckily for you!), and that is to another Oneworld airline. If you had been flying UA on LHR-JFK than BA would not check bags through, but they will for AA. You are OK in both directions, but be sure to have the ticket number for both tickets with you (not just the PNR locator, but the actual ticket number, that would be in your confirmation email for the e-tickets).

LHR transit took under an hour this week, at noon. It looks like the really huge queues are limited to morning (say 8am to 10am) and late afternoon/evenings. It is fast at 6 am (first flight of the day in) and to my surprise was pretty good at noon. Travel volumes may also be lighter now that it is October.