If you are on one ticket, yes AA will check your bags through to QR and your final destination. If not, you will have to pick up your bags in BOS and recheck in with QR.
QR does require you to "exchange" your AA issued boarding pass to a QR one. You can do this at the gate before boarding. Your AA issued one will get you into the lounge.
Yes, QR does use AF lounge. One of the worst lounges I have ever been in. Is very crowded that time of night. If the BA lounge is open, use that lounge. Much better experience, but I have been given push back to get in. Didn't Chase just open a lounge in BOS? If you have access to that, I would definitely try there.