I'm running a circuit into a new half bath. My plan was to run two outlets in the adjoining room then to the GFI in the bathroom then to the switch, 2 vanity lights and end at the vent fan.

1) does it matter if I run the switch, lights, and fan off the load side of the GFI? Or do I have to pigtail in the GFI box?

2)is there a restriction on placement of the switch in relation to the sink?

The pedestal sink is centered on a 4 foot wall. That wall is only 7 inches to the right of the pocket door. Unless I notch a 2x4 there is no room for a box on the door wall so I want to put the switch on the sink wall. I hope that makes sense.

3)I'm guessing a 20amp circuit is required here (hair dryers, curling iron etc). Correct?

You will need 2 circuits for this, the bathroom outlet should have it's own 20 amp breaker and the rest can be on a single 15 amp. Code requires bathroom outlets have their own circuit. Might seem strange till you figure out that a hairdryer alone could draw 15 amps. I know this is a half bath and as such is unlikely to have a hairdryer in use but the code to my knowledge makes no distinction between full and half bath.