Can I Access Both My Own Library and My Friend's Library?

You have to configure your remote access for your server. If you have already viewed your friends server from your house that means he has already done that

https://support.plex.tv/articles/200289506-remote-access/

If you have trouble look over these guides
https://support.plex.tv/articles/200931138-troubleshooting-remote-access/

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