That's not good Gilly, you could probably fill that hole up but you'd need to slip some veneer into either side of the neck pocket to take up those gaps and then sand it back evenly to get a good fit.
The Nut, well that just looks really bad.
It is normal to have the gap under it for the truss rod channel so I wouldn't worry so much about that. it does look rather decidedly wonky though.
I'd be stripping that off and looking at the underlying wood. to see if it's a case of:
a. just a bad nut fitting job
b. an issue with the mounting surface under the nut
c. a Cr@p nut with an irregular underside
**EDIT**
Having taken a close up look at that front edge of the neck pocket I'd be really concerned about the side veneer and the roughness of the top edge where the fretboard/Neck will meet it. It might pay to draw Adam's (PBG Dude) attention to those spots.
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