When you're dealing with a department that size, there are no easy answers.
In regard to bureau, it cannot be determined by the plate number alone. However, the side of the car generally reads something like, "FSD 300022." This would mean the vehicle belongs to the Fleet Services Division (FSD), the RMP number (plate number) is "3000," and it's a 2022 vehicle. Those letters can be used to determine what bureau the vehicle belongs to.
By and large, RMP number does not indicate a call sign. However, I have heard, and perhaps a local can confirm this, that some divisions, such as Parking, sometimes use RMP numbers, i.e. "Smart Car 2707."
There are a couple threads on the Forum detailing NYPD call signs that you can probably dig up with the Search tool.