1) At the moment, each site within the app is actually a combination of user and site. This means that you can for example have two "sites" configured in the app that are in reality the same site using different accounts. One drawback of doing this that you'll have to download the content for offline use two times, once per account.
2) Yes, but make sure that the Moodle sites are not configured with the "force logout" option in the mobile app settings.
3) Not necessary .