Lots of good advice here; I'll just give my thoughts after having built up my '02 600 RMK into a 144 with a mix of used, rebuilt, and new parts. I'd pull everything apart, check for bent pieces (I had to straighten my rear torque arm), clean out all the pivot points, and replace or rebuild the shocks. Unless it's a top spec model, it just has basic, non-rebuildable shocks. They may not even be gas shocks, in which case they won't rebound on their own. Either way, you can tell if they're bad if there's a big range where they'll compress or rebound with little resistance. Most sleds have never had the shocks replaced or rebuilt, so I'd anticipate replacing them. Before you buy basic replacements (and I'm having trouble even finding those), look into finding some RydeFX rebuildable shocks. I got a set off an '03 Vertical Escape, and after a rebuild, they're by far the best shock you can put on an Edge RMK short of a very expensive custom shock.
As to the torsion springs, assuming it's not other things causing the lack of rebound, then the springs have probably sagged. Some guys, especially "bigger boys," step up to the .375 spring as a matter of course. Maybe not a good idea for a lighter, more laid-back rider, but suggested for someone who likes doing jumps and things that tend to bottom the suspension. One test to do is to see if you can get the specified amount of sag by measuring the rear bumper height, then having the rider jump on and bounce on the boards a few times, then measure the bumper height with the rider still on. You should have around 4" lower height with the rider on. Also, if you crank the adjusters to their highest setting, the suspension should be pretty near full extension: if you can lift the rear more than a couple inches with the skid still on the ground, the springs probably need to be replaced. One other option is to bend the current springs to get more preload. It may weaken the spring, but I've done it with mine and rode a couple seasons without issue. You need a sturdy vice and big piece of pipe to do that. Clamp the spring as near the coil as possible and bend the long end downward, giving it another 10º or so at a time. Obviously, use common sense; if you're not sure what you're doing, there's a strong possibility of breaking something and/or hurting yourself.
As for the handlebars, I think they're the same size, but I've never attempted the swap. A handlebar riser might be a better idea, but either way, volcano is right about the steering post. I've done ok, but it's a known weak point, and taller bars contribute to that (the taller you go, the more leverage you apply to the steering post).