For (1)
polygon = Entity["City", {"NewYork", "NewYork", "UnitedStates"}]["Polygon"]
points = List @@ First@polygon
For (2), do you mean something like this?
nycPosition = Entity["City", {"NewYork", "NewYork", "UnitedStates"}]["Position"]
GeoGraphics[GeoDisk[nycPosition, Quantity[50, "Miles"]]]
