yes it does after about 4 hours or so
If it is an iPod Touch, yes, you can work on an iPod or use the iPod while it is charging.
It's hard to tell when your iTouch is done charging, but the battery bar should be green all the way full.
because its not plugged in
yes you can
No, each iPod Touch comes with a charging/data transfer cable.
Your iPod will automatically turn on when you plug it in and start charging it.
buy a a new one
Yes, you can. Like most electronic devices, you can still use it when it is charging.
try charging it or connecting it to itune
It means it is charging.
mayby your battery ran out try charging it