Would Candidates Searched for a given Weyr come from that Weyr's hinterland only? For example, would River Bluff dragonriders ever take Candidates from Dragonsfall's Holds and Halls?
Not without special permission. The Weyr the Hold/Hall is beholden to has exclusive rights to Search in their territory. The candidate could ask for a transfer if they have family at another Weyr or some other special circumstance, but it would be up to the Weyrwoman I should think since she's in charge of candidates. (I will have to check to be sure that's who you'd need to ask, though)
Yes, they would need to have the Weyrwoman's permission of the Hold they are moving to.