Hello wljt
The SBB Mobile App works even without an internet connection. Taking screenshots is fine, as long as they are scannable. There is no need to print the tickets, but you must carry your physical passport (no copies / no photo) with you when using e-tickets. They are valid with a physical proof of ID only.
Also, keep in mind that the Supersaver tickets are only valid for the connection as indicated on the ticket; they do not offer flexible travel plans.
Best regards,
Roland