I don’t think I can agree with this part, although “fairly base” is always in the eye of the beholder, 
… It’s definitely way more than apt-get install postgresql, though.
I’d suggest SSHing in and then poking around a little with ps aux, ss -tnpl, etc.
No, but the docs really do lead people in that direction… In reality, it’s the port for when you don’t care whether it’s writable:
Try cloning a node into bos, and then you’ll see the distinction way better.
If your overall aim is to spread queries out evenly over all 3 ewr machines, then I think Fly is expecting you to query db-app-name.internal (not .flycast) and combine with your own round-robining.
Conversely, if you did specifically only want to connect to replicas for some reason, then the (relatively) new metadata-based DNS queries may eventually allow that. (At a glance, it doesn’t look like the roles are currently getting published there, although some generic minutiae are.)
Hope this helps a little!