How tall are you houyi? In any case, when you're looking for a new car tell the salesman you'll be sleeping in it from time to time, fold down the seat and see how comfortably you can fit. Dieter's advice is spot on although I'd add that "air mattress" should really be a Therm-a-Rest style blow up sleeping pad. Those are surprisingly comfortable to sleep on - you can get them a couple inches thick and they're wide enough for you to fit on and narrow enough to fit along the back of the backseat that you've folded down.

As for working out, you can do a lot of exercises with resistance bands if you're wanting to do anaerobic stuff and they don't take up much space at all. But sure, you can do a search for Anytime or 24 Hour Fitness (~$40/month) and see what kind of coverage they have in the areas you're planning on hitting. If nothing else you can shower there whenever you need so even if you never work out it may pay for itself just for that.