1. Bluetooth probably won't be able to give you good quality audio and mic input at the same time. It doesn't have enough bandwidth over a single channel, last time I tried. Of course that was probably like 5 years ago and things might've changed, like a theoretical workaround I thought about is the headset simply having two bluetooth reveivers and connecting twice. But yeah.

Edit: I suspect jgrffn's comment in the thread refutes the above. I might test later.

2. Most of the proprietary wireless 2.4 ghz usb adapters I have tried have worked fine and better than bluetooth since they can do good audio and mic at low latencies. I have used logitech and corsair but my logitechs died on me (one I bought had the left side die and the other the right side :/) and the corsair earmuffs fell apart after I made the mistake of not being perfectly dry once. So I can't really recommend my most used headsets.