ATV is limited to 2 bluetooth connections, but you can connect additional devices through your smartphone running the Zwift companion app.
I've not done this, but others on the internet suggest it works fine. Not sure what happens if you're also running other apps on your phone. (I use my phone for music, etc while riding).
There's no need to use your Garmin head unit while on Zwift. Zwift will record the ride and can then upload data to whatever platform you're using (Garmin Connect, Strava, etc). Recording on your Garmin would just duplicate the info.