A can on it's own makes more noise and, if you're lucky, the same power as standard. The de cat headers seem to give a bit more lift near the red line, plus a slightly raspier exhaust note even with the standard can.
Many of us have cut the standard headers, removed the cat and had it re welded. Works just as well as spending lots of money on a Remus, etc. You can easily pick up a set of standard headers on eBay for not much money if you want to keep the originals. That's what I did.
Even with the de cat headers and/or noisier can, the engine will still be running as lean as it does standard. The bike's ECU compensates for any changes you will make. Won't blow up, but will still be harsh, have a flat spot and surge now and again.
They all do that, sir.
As greenman says, you'll get most benefits from fixing the fueling.
Choices are a re map, Hilltop is the preferred around here but make sure you're keeping it for a while.
Power Commander, works well but issues with lots of connectors that can take in water and cause problems. Bit obvious if you 'forget' to tell your insurance company.
My preferred is the AF-XiED units. These manipulate the signals from the O2 sensors to enrich the fueling by up to 8%.
All have similar costs and will turn your bike into a smooth, torqey thing.
Forget booster plugs and similar. The ECU will adapt them out after a couple of tanks of fuel.