basically, your assumptions are not that bad:
1) CPN/CPP are for the charge pump. As it is not possible to integrated the required capacitor for the charge pump directly in silicon, an external charge pump capacitor is connected to these pins. The application diagram in the TMC223 datasheet (www.trinamic.com
) shows how to do it and what capacitance you should use.
On the other hand, VCP connects the external charge pump filter capacitor to VBAT.
2) VBAT pins: Although the name "battery" supply voltage is a bit misleading, this is the supply voltage for the drivers and the motor.
3) This is an input for a reference switch (if you have one in your application). It is NOT to tell of the motor is on or off. This pin is not digital. See the application diagram in the TMC223 datasheet on how it is connected.