The nut on mine had such little glue holding it that it was loose by the time it arrived. If yours is anything like mine it shouldn't be too hard to get it loose.

The neck pickup cavity is kind of a problem, yeah. The cavities are shallow and I'm not sure there will be room to route the cables under the pickups once they are screwed in. I expect to have to route a spot for them.

Scale length is odd. I'll remeasure with a pickup in the cavity when I get a chance but when I measured before on mine it looked perfect on the high E side and concerning on the low side. My best guess is that the "27 inch" scale has compensation for saddle needing to be back further on the heavier strings. If not I'm not sure it will go back far enough.

That neck pocket damage is really rough. I would definitely be seeking advice here from someone who is better with wood than me, but that will be difficult to make look good with a stain or dyed finish.