Cut off filter effect all parts?

IIRC, the 6 assignable knobs only control the currently selected zone. In contrast, the modulation lever and control pedals affect all zones with keyboard switch enabled. I would try that first. If you need a knob/slider, then you can consider getting one that can be connected to the control pedal connectors, for example Loopop's Plus 3.

Very possible. Use the mod matrix / aftertouch via an expression pedal. Set up all patches in your Studio Set so the mod matrix will allow an expression pedal to control filter cutoff via Aftertouch. (Just set it to Aftertouch if you're using the PCMS engine and you can control many parameters at once.) The SN-S engine is not as flexible but has filter cutoff under aftertouch to accomplish the same thing.