

Yes. GMT is UTC (meaning GMT is +0 and synchronized with UTC), therefore if you have to work out what time it is in other time zones, you use UTC. Your application shows the time in your time zone (unless otherwise specified). Responses will also be shown in your time zone.
I, too, run an always on VPN from my mobile devices. I can still access my home network with pihole and DNS entries to my services. It’s not that difficult. I agree though, mTLS is a good option.