1) this is most likely because you are running a brand new cog with a chain that has mated to the other cog, how long have you ridden this chain? also if you are running this chain too tight it will only make it noisier.
2) are you running 3/32 or 1/8 on the chain and cog?
3) i have no idea what you mean by wobbles back and forth, i would check to make sure your wheel is centered.