I think that you could go either way. For me, my only concern would be while using the sink if it protrudes too much ( which yours do not appear to ). Guess it’s a matter of personal preference, some would like the uniformity of adding, others, like me, wouldn’t care, actually I like it without.

If it gets in the way, not. If it's a handy place to hang a washcloth, yes.

are your sconces upside down?

I would for continuity as long as it doesn’t protrude.

Leave it blank.

This is why I like to do full height doors for the sink cabinets.

No it is not a sink fake drawer but rather a sink skirt and if you look at most wood vanities with this panel it never had a knob as that would just accent it.

I too like full height doors there but it really is just to each his own, no rule .

No.