AA lists the jfk-zrh (flt. 64), as arriving at an A gate--which is never the case. This flight is immediately turned around as flt. 65, and this flt. leaves from an E gate.
Re lounge access, the Dnata lounge is the only "official" AA lounge.
If you have Priority Pass, there are lots of other lounges, the most convenient is the Panorama Lounge, located a short distance from the E gate, AA will use for departures.
I believe this information is out-of-date, (It
used to be true.) As of March when I was last there, there is a new OW Lounge directly across the hall from Dnata, and that is the "official" AA Lounge. Dnata is still open to PP holders, but the OW is a bit larger. Neither has showers.
I have also seen the "A" gates listed for arrival, but also doubt the accuacy of that information. I've always departed (and arrived) from "E" gates recently.