Lots of questions, Adam. (1) Black mirrors are the easiest ways to get in touch, and you just have to have personal discipline not to react real-time to the pings you hear. (2, 3) People appreciate a heads-up so my auto-response indicates my current time zone. I run weekly check in calls with my team, when I’m off-work I still skim emails every few hours for emergencies (which most people do anyway). (4) Planning in advance of a trip (even on the flight there!), getting reccs from friends and letting go of FOMO where I can. You’ll never fully experience everything in a city.
If you’re not able to work remotely but want to, I advise you to read the vast body of how-to literature online about making that transition.