Explain what happens when I reboot an EC2 instance?

Rebooting an instance is like rebooting a PC. The hard disk isn't affected. You don't return to the image's original state, but the contents of the hard disks are those before the reboot.
Rebooting isn't associated with billing. Billing starts when you instantiate an image and stops when you terminate it. Rebooting in between hasn't any effect.