How tight should studs be when framing in place
I assume that you're referring to interior, non-bearing walls, such as those in a previously unfinished basement. Ideally the studs will fit just snugly enough to hold them in place as you nail them in. You're right that you can jack up the floor if you force them in, but it's more likely that they'll bow a bit. 

If they're slightly short it will be more challenging to nail them in accurately, but it won't likely cause any issues. Most of their function is to support drywall, and they'll do that just fine.  You can always pop a shim in at each joint, or squirt a dab of construction adhesive to fill the gap.