9. Is it possible, at least in isenthalpic processes, that the Wet Bulb Temperature (WBT) is independent of the relative humidity?
Yes, it is quite possible in ideal cases when, as you said, the process is isenthalpic. Wet Bulb Temperature (WBT) is the temperature of a parcel of air when it's completely saturated with moisture when the parcel is enthalpically forced to absorb moisture.