There isn't much in a rear sprocket that can reasonably be fixed. Most common action is simply to replace it. You need the correct freewheel puller to get it off though. www.parktool.com has a page about repairs and tools.
If your problem is that its sticking or not engaging you can try to flush and relube it. Put bike on side, flush plenty of WD-40 or similar through gap in freewheel, see if you get any gunk out. Then dribble in some runny oil(engine oil will do) and see if it helped.
One can fix a Scott Mountain bike when one goes onto the site of Bike Rumor. There, one can find reviews of bikes and more importantly, one can get tips on how to fix one's bike.
500$
It will if you have bmx (or bmx style) cranks.
jcs or any bike store
There are too many possibilities to be covered here, can be anything from a worn chain/sprocket, to a stem or something not being proerly tightened.
The chainring by the pedals and the sprocket(s) by the rear wheel.
25t means that there is 25 of the little spikey teeth on the outside of the sprocket :]
Chain is on the smallest sprocket on the crank and on the largest sprocket on the rear wheel
it would depend on whither you are riding on a mountain bike or something that wont be doing stunts or a bmx or dmr. for mountain bike it probably will not matter whither it is big or not however for bmx or dmr it would be a good idea to have a smaller one as when at skate parks eg. you where going to drop into a bowl that is quite steep if you have a big on then the chances are it is going to hit the coping (top of edge) and maybe fall off. also if you are thinking of getting a smaller sprocket you will need to get a smaller cassette but don't guess how big the cassette should be for a sprocket just take it to a bike shop and they should be able to tell you. for a smaller sprocket i would recommend a 25t to 30t,, the 25t will have to have about an 8 or 9 tooth cassette. hope all of this helps took me a while to type out anyway :P!!
First gear on a bicycle with external/derailer gears is with the chain on the smallest chainwheel(by the pedals) and the biggest sprocket(by the rear wheel).
Not a sprocket only, but you can buy a 23-tooth freewheel that should fit.
you would first take a marker and put the sprocket on the ground and where it is bent mark it then put the sprocket on a flat space and heat the part where it is bent take a hammer and hit it soft it should fix it right up