Exhaust? I'd say tomei, but only ever heard it once a while ago.
Coilovers vs lowering springs...
Ok first off what do you use your car for, and what is your goal. If you just want lower, but keep comfort, general consensus is go with springs. If you want really low, and don't care about comfort, coilovers.
Now, from what I've heard, you can get both with some coilovers. Brands that come to mind are kw (or st), and rsr. But neither give you slammed. Coilovers are not good for winter driving though.
Third option you didn't ask about but you might consider is air. I like that method. Adjustable on the fly. And just as good as coilovers supposedly.
Sway bar vs strut bar.
Yes there is a difference.
Sway bar is a torsion bar that twists to basically push one side back down to the ground to help keep the 4 wheels on the ground. This part helps with body roll.
Strut bar is pretty much just a piece of metal. It helps keep the chassis rigid and keeps the body of the car from twisting and distorting. This is considered a chassis upgrade. It follows the same idea as a strengthening beams
Crank pulley
Don't. Waste of money and time. I've had it on my 08 impreza. No difference. It only looks pretty.
As for increasing acceleration, not much. Your car is slow. Not to be rude but deal with it. You can spend 5 grand and get an avo turbo kit, but I don't know how good it is. You can put in a fancy intake, exhaust, and maybe tune. But you won't change much but decrease driveability. Believe me I've tried. Don't waste your money. Save up and buy a wrx or sti.
Can't stress that enough. I once thought about making my impreza really nice, but realized that I can go so much further with a wrx or sti. With the same amount of money. If you can afford it, go sti. You won't regret it. Only get a wrx if you want something from it that the sti doesn't have. For me it was the sunroof. That's all.
