All backs are different, all back problems are different. Recumbents may, or may not, relieve stress on a bad back, depending on the problem and the recumbent in question. As mentioned previously, they're all different, too. They have one thing in common: they all have seats with backs for support. If you have a back problem and an upright is making things worse, maybe a recumbent would help. Or not.

Do not expect any bike, upright or recumbent, to keep your core muscles in shape. Bicycles are great for cardio and leg workouts; in fact, they're not very good for building leg strength either. Toning and endurance, but not strength. They pretty much suck for any other parts of your body. For a full-body workout, I recommend swimming. For core, do calisthenics. For most people, doing sit-ups is the best way to prevent future back problems.