Build number (lucky) 13 - AST-1SW

[McCreed]

The nut does look a little off-centre to me too, but as for the pocket end, that should even up with a bit of a nudge down (toward treble E) from the headstock end. I've seen worse.

The veneer looks a bit thicker than I was expecting if I zoom in the routed sections.

I'd say that looks about right. The veneer is generally .6mm.
IMO, I think people get way too paranoid about sanding veneer. You just can't dig into it with 80 or 120 or go hard with a RO Sander.

Edit:
I meant to add, that's a nice looking kit too!