As for the described remote access issues…
Did you already have a look at the related troubleshooting support article?
https://support.plex.tv/articles/200931138-troubleshooting-remote-access/
There’s also a guide with some more details on how to troubleshoot remote access issues. The individual findings should help to pin down what’s causing this for you (given there can be many culprits). We would need those details to help you further.
As for having to navigate to More in order to access your library… simply pin the library from More and it’ll show up in the main navigation/sidebar.
Here’s an example of how this can be done in Plex Web. The approach is the same or similar in other Plex apps.
