I will check the neck angle again - just to be extra sure. When I checked it last time, I put the tune-o-matic bridge in place just with some tape around the posts and tried to set it at a height that resembles the lowest height when it is installed. I then put a long straight edge on the clamped neck (on the fretboard that is) and checked how it runs towards the bridge. When the straight edge lays on the fretboard it touches the bridge - I thought that this might be ok. I'll make photos when I check it again.
1. Yes, that is what I was planning to do: glue the neck and then fill the gap. Of course that means that the gap might also be filled with glue after putting the neck on, which might lead to a slightly awkward staining picture. It's really only a small gap, so I think it won't be that bad.
2. I already checked that. The fretboard is parallel, so I hope this isn't an issue.
3. Will do
4. Ok, I'll give it a try. Do you think 240 grit is ok?