I see a number of Robotic Hand Kits for sale (including 1 here), but none of them talk about the power source for the servo motor(s).

What kind of questions should I ask a seller about the required battery?

Are the connectors for these batteries "standard" to plug into the servo-controller board?
Is there some generic servo-controller board out there that can be used for a wide variety of servo-motors, or are the controller boards specifically matched to the servo-motors they were designed for?