Plenty of videos and info for the stage 2 S5/S4
Stage 1 is just a remap of engine and gearbox = about 440bhp
Stage 2 is bolt on parts. About 460-480bhp
Stage 2 in most cases is a supercharger pulley swap. It used to be that the charger pulley was replaced, but it makes more sense to replace just the crank pulley as this is available in loads of sizes right up to the max ratio and flow of the super charger.
For a good Stage 2 setup, you need a bigger crank pulley which will take the speed ratio of the SC to 3:1. Intake modifications, best value is to replace the intake pipe, fit a free flowing filter and add some holes to the airbox, then mapping.
Stage 3 would be either porting the supercharger or fitting a larger throttle body and possibly going bigger on the crank pulley to up the SC drive ratio. You may hit the 500bhp, but to eek out the smaller extra bhp, you spend a lot more money. Basically each stage means more money for less power increase. So most will stop at stage 2. This is a decent amount of power! I remember when 400bhp was Max Power front page stuff!!
When you go to stage 3 and push the SC ratio over 3:1, this is when inlet temps can go high and more so in warmer climates, then you need to look at larger charge coolers.
I believe it is earlier cars that had issues with cats melting on stage 3 cars or crap fuel, or pop and crackle maps!? A good stage 2 will be fine with the cats.