About charging - you would probably need a separate charger for the laptop, as:
1. I would expect HPs connecting cable (which is basically a bundled Thunderbolt 3 connector with the power supply connector) to be incompatible (physically) with ASUS's connector.
2. Voltage-wise they are also not identical (19V on ASUS vs 19.5V on HP) - that's pretty close, but there is always a chance there is something more to it (i.e. I'm not an electrical engineer).
Apart from that look around in the comment section if others tried connecting the docking station with just a Thunderbolt connector (+ separate power supplies to the station and laptop) and if it worked for non-HP zbook models. I don't have any other Thunderbolt 3 compatible laptop so sadly I can't test, but it might be possible (unless HP put some proprietary stuff there, which I don't expect).