2. Depends on the size of the breaker or fuse feeding this. If it is 15amps, then yes. If it's 20amp, then you need 12/3.
3. You can get a clip or screw to tie the ground wire to the metal box, unless there is already ground wires present there. If so, you tie the ground to them. At the switch, just tie the bare wire to the green screw.