Am I permitted to wear a watch on shabbos in an area that does not have an eiruv?
Yes.
Would the same Halacha apply to a automatic watch that works by the movement of the hand if yes would it be permitted even if the watch stopped before you put it on is there a concern of makeh bipatish like the MB says in siman 340 or does the Rav rely on the panim meiros
Yes. Even if a regular old fashioned wind up watch stopped on shabbos, he holds you can wind it. Similar to a baby swing.