Per the books, there are at least hundreds, maybe thousands or tens of thousands. Starks have been burying their dead down there for generations. In the books, we only see two levels of the crypts, but there is mention of multiple levels deeper than those levels, with the most ancient Starks being buried very deep below Winterfell.
He was very far away from the bodies he reanimated at Hardhome. But, he did have line of sight, so maybe he has to be able to see the dead to raise them.
Unless I am mistaken, when Jon took a group of adventures north of the Wall to capture a Wight, there was discussion that they had to capture one without killing the White Walker that was controlling it. Therefore, I assume that all of the White Walkers (there looked to be a lot of them at the end of last night's episode) can control the dead, and may be capable of raising them (I know they can in the books).