Those gaps at the heel/pocket are quite small IMO.
If the neck fit is snug, but not so much that you have to force it into the pocket, that's fine. You'll need a tiny bit of movement to be able to align the strings properly before permanently setting the neck.

As for the gaps, I'm presuming you will have a contiguous base and/or top coat that extends from the body to the back/sides of the neck. Those little gaps should fill in with the base and top coats when applied.

Since you're painting and not staining or going for a natural finish, and if the gaps bother you, you could rub a bit of Timbermate in there once you've set the neck and before you paint.


re: the neck pickup
You need to check your scale length and see if the neck can be to moved away from the bridge at all. If so, it might be enough to allow the pickup and mounting ring to drop into/over the existing p/u route. If not, then a little bit of extra routing may be required to get the p/u to fit properly.

Apparently this is not an uncommon issue with some of the set neck kits, but completely workable. I encountered this with my PRS-1TS kit.