Yes, everything works fine, but you need to set up the connection correctly first, so that the camera immediately detects the bluetooth connection.

I do not know and I am wanting to sell it with the camera I bought it with but Galaxus is making me sell separately. It came with the Sony ZV-1F

Yes, I use it in this combination.

Unfortunately not.

At the competition, the same product costs up to 200 Fr: https://www.toppreise.ch/preisvergleich/Sonstiges-Zubehoer/SONY-GP-VPT2BT-p610965

Nein: https://support.d-imaging.sony.co.jp/www/cscs/accessories/compatibility.php?area=eu&lang=de&mdl=GP-VPT2BT&cat=1&loc=de_CH

Good question. If the manual says nothing, then Sony must have forgotten something: https://helpguide.sony.net/ilc/1970/v1/de/index.html

Yes, sure. Anyway, it works fine for me with the RX100 VII.