If it's a singel speed, or internally geared bike it might very well be called a sprocket. If it has external gears it's either a cassette or a freewheel. It might eve be a freewheel with only one sprocket on it.
It hooks the wheel to the chain, which is hooked to the chainring by the pedals, which is what makes it possible to set the bike in motion by pushing down on the pedal.
Pretty much whatever you feel like. Do you want to go faster, but can't spin the cranks any faster? Get a smaller one. Do you feel like it's hard to get the bike moving? Get a bigger one.
On a bike there's one(or more) front sprocket(s) by the pedals connected by a chain to one(or more) rear sprocket(s) by the rear wheel. As the wheel isn't driven directly by the pedals, and there's usually a difference in size between the front & rear sprocket this constitutes a gear.
The chain is size 530, and the stock gearing is 15/45, meaning that the front sprocket has 15 teeth and the rear sprocket has 45 teeth.
No way of telling, it depends on how strong or high revving the engine is. Switching to a bigger front sprocket might make the bike faster, but only if the engine is strong enough.
It uses a 47 tooth sprocket.
41 tooth
No way to tell, as it will be different depending on bike size and sprocket tooth count. Bike chains are always sold overly long and are then cut to size.
Depends. Usually there's some leeway for adaptation, but it's possible that your bike was delivered with the smallest sprocket available for that hub.
Press down the rear foot brake and use a breaker bar or large ratchet with correct size socket to loosen nut on front sprocket. (never use impact wrench NEVER EVER!)Once you get the nut broken loose. Unclip your chain and put the gear in neutral and pull the chain through and set it aside. Put clutch in first gear and continue to ratchet loose the nut. Loosen nut all the way. Change out the sprocket. Tighten nut as much as you can with bike in gear. Put your bike back in neutral and feed your chain around the sprocket pulling it through and resting both sides of it on the rear sprocket where you will reclip the master link. Meeting both sides of the chain on the rear sprocket will make it easy to clip as the rear sprocket holds your chain for you. Once master link in chain is clipped. Step on the rear brake and crank down to spec lbs on the front sprocket bolt. If you don't know the foot lbs.. just make sure its real tight. Your done!
They came stock with a 49T or 48T rear sprocket you can choose a replacement with either a 48T, 49T, 50T, or 51T, if you have the old sprocket count the teeth on the sprocket and that tells if it is a 48T, 49T or whatever (48T = 48 teeth)
13 tooth front/ 40 tooth rear
45 tooth rear
25/9 gear ratio