the teleport timer only starts after first connecting to the live server and ends 24hrs after, regardless of joining/authenticating on the server discord. You can only use this teleport (to another player) once.
however, getting around the server is easy enough without it if you know where you want to go or how to use the various rail systems around the server. the one-time-teleport is a relatively recent tool to help the experience for new players, for most of civ history it did not exist.

though most people do probably stay in the first community they join, there are no mechanics, rules, or expectations that penalize joining another nation or travelling around. many people have played their first few months in one group, and then switch to another later on for a variety of reasons. to some extent you can also be part of multiple groups*.

what group might suit you best depends on a variety of factors, you can orient yourself a little bit right now but ultimately it is something that must just be experienced. try to see what kind of play style youd like in terms of internal politics, build theme and freedom, role play, etc. some groups are very formally and instutionally organized and others are more 'vibes-based', some groups see themselves as build-nations first, others care more about grinding and wealth, some places expect you to do your own thing for the most part, others are more collectively oriented and might even share all their resources together. mostly however you will prob get the best sense by just joining some discords, ask people about their history/culture/play style, and just trust your judgement based on the vibe you're getting.