How many modulations can a particular slider or other controller affect. For example, have one slider modulate LFO depth and filter resonance or somthing.

yea. The four sliders, along with the velocity, aftertouch, and pedals can be set to change whatever you want.

Cool! Can these controls (velocity, aftertouch, ...) change more that one thing at the same time? If so, how many?

Yes, you can assign up to four parameters per tone to be controlled simulataneously by one controller and the "depth" of control can be adjusted for each parameter as well.

Go [PATCH]...[F5: LFO&Ctl] and you can see how you can select the parameters, etc. for up to three controllers per tone.

If you choose to use a system controller (SYS-CTRL 1 or 2), specify it at [SYSTEM]...[F4: Control].