For the APP_BASE_URL, you should use whatever the address will be through the proxy. So in your case that would be http://your-nginx-webserver/joplin.
Regarding the login, what storage backend are you using? Are you using the PostgreSQL backend? I haven't used the SQLite backend so can't give feedback on that. I haven't encountered any issues with the Postgres one. I use a second user I created for my Joplin syncs.