-No, other sites won't cause issues, regardless of what they are.
-If the individual bookmarked the site and tried to return, as long as they were within their session timeout they'd get right back in. You can set the auth cookie to not expire, and can use persistent sessions to keep them logged in indefinitely on the server.
That said, IMO it's a bad idea to have infinitely-persistent sessions: they take up extra storage, and are a security issue.