Unhealthy people pay more (kinda fair don't you think?). Healthy pay less. Some have additional motivation to get healthier, because "screw the old me, I don't care about that looser... but if I move a little I can pay less now? Tell me more!"
Average society healthiness increases. Even worst scenario is great.
Depends. You can be unhealthy through no fault of your own (genetics, environment). From social utility POV, insurance is about pooling risk. Taking your scenario to the limit, if insurance company is able to compute an accurate risk factor for everyone and adjust premiums accordingly, then the risk pool evaporates. But then again, maybe health insurance shouldn't really be a private industry.
Risk is still pooled because payouts come from fees of the people that didn't (and won't) experience costly events themselves.
More information just makes the business more just and less random for insurer.