Can the s2 mk3 be mapped to emulate a xone mixer?

Yes. Go into Preferences→Controller Manager. Select the S2 mapping file from the dropdown. It's empty, ready to be overmapped. Click 'Add In.. → Mixer' to select the eq controls. If you want to use the Gain knobs for both Gain and HiEq via shift, you have to use modifiers. Select the modifer assignment for modifier 1. Assign it to the SHIFT button, type button (hold) value 1. Uncheck 'override' (so it adds the modifier function but leaves the factory mapping SHIFT function untouched). Next you add modifier conditions to the gain function (M1=1) and the HighEq function (M1=0). Both should have Soft Takeover checked.

Yes, you can do that without modifiers. You can rearrange the functions of the equalizers and FX knobs and buttons since they work without the SHIFT or DECK layers easily.

You should know that the S2Mk3 and the S3 don't have FX controls. You would have to use the MixerFX/Filter knob for the mapping if you don't want to use the Gain Knob. Check out some pictures of the controllers and you'll see what i mean.