If you buy an economy ticket, expect to go economy. You will not in general be upgraded just because you have OWE status. Infact I wouldnt be surprised if BA is less likely to upgrade you as a OWE, because there are anecdotal reports that if an OpUp is necessary, they often pick regular Y flyers to give them a taste of a premium cabin so perhaps they will pay for a premium cabin ticket next time. If you are a OWE, you presumably know all about premium cabins already. If you want to go premium economy, then buy a premium economy ticket.

I can't comment on what AA do for non-AA OWEs as I use the AA program.

If you are OWE, you can use any OW first class lounge. In T5 LHR (if you take BA) then that is Galleries First (next to the Concorde Room, not the other Galleries lounge at the opposite end of the terminal) or in T3 LHR you can use BA Galleries First or the AA Flagship lounge, or the CX lounge if the refurb is finished by then.