User Manual TP-Link ‎ARCHER T4U PLUS Dual Antennas High Gain WiFi USB Adapter

It is usb so you could try, I didn't get any detection on a pc. I didn't spend much time with it so I am unsure if it works. The xbox already has wifi built in and it works fine to out router.

If you are asking whether you can use this adapter to connect your computer to a WiFi network that your jetpack is broadcasting, then yes.

No, it only provided the adapter.

No. You'd need an Intel card or Buffalo card buikr specifically for security scanning tasks.

Probably it's the settings in your computer that identify which band you prefer to connect to. We have found that sometimes our Windows computer switches between bands without our specifically requesting one or the other.