You might have trouble getting free unrestricted library cards if you don’t live in the area that the library serves. They are usually paid for with taxes and aren’t there to serve people outside their community.

If you’re willing to pay for it, I know that the Ottawa Public Library in Canada offers membership for $90/year to people living outside Ottawa. You may find something similar at other libraries.

The Libraries and Archives of Canada will issue a card too, but you have to visit the archives in person and have a reason you are using the archives and not another library.

That depends on your goal. If you want something free, open source and self-hosted then Plex isn’t the best option and you’d do better to look at Jellyfin or Kodi.