1) Yes, as long as the circuit does not leave that ONE bathroom.
2) No. You can share the circuit with other baths if the circuit is just feeding receptacles. If you include any other bathroom loads then the circuit must be confined to that one bath, as said above.
Sometimes I feel like if I answer any more questions it is like someone trying to climb over a fence to jump off a bridge and me giving them a boost.
Answers based on the 2008 & 2011 NEC.