first off welcome!
...secondly, whoa! overload of questions. you can split them up in different forums
The intake and exhaust is a nice start, but when you mention intake do you mean an intake manifold? '01's already have an LS6 which is prime performance for moderately to heavy modded LS1's.
obviously "full exhaust" would be the best choice and as you will gain with just a catback but headers will really let her breath. longtubes and true duals have no issues with clearance BTW (at least stock ride height) otherwise lowering springs will contribute to more cautious driving.
also when all of this is bolted up, get a dyno tune if you're able to as it will cost just about the same as picking up a handheld and more than likely will net you better results.
hopefully some of this helps...