Does back surgery help with back pain and can it also correct the spine?

Instability. For patients with instability of their spine refractory to conservative management, fusion can be a good surgical option.
Depends. Depends on the injury and the efficacy of the surgeon; there are good "minimally invasive" surgeries for backj pain that may not require a bunch of hardware; look for minimally invasive back surgery in your area but if you have a compressed nerve it may be the best solution. Get a couple of opinions, though.