The initial G in the model seems to indicate a particular factory and whilst their general body construction seems to be of a higher quality, lack of bridge grounding holes does seem to be a speciality of theirs.

Sanding the end of the neck is fine, as long as you do it before positioning and drilling any holes for the bridge. It's worth checking the fit of the pickguard around the end of the neck as this may cover up the current gap, and if so the pickguard does fit at the moment, it will also need some modification if you reshape the end of the neck.

Neck screw mounting holes are best done in two stages. First drilling through the body using the neck plate as a guide for screw hole location (you'll be surprised how badly the factories line up screw holes with the holes in the bridge plates on the factory drilled kits, so doing your own if preferable IMO). Use a drill size that's as wide as the screw. You want the screw fitting just fitting through the body without binding at all, so that the screw can always pull the neck down firmly. Ideally use a drill press or drill stand to get the holes vertical, or a metal drill guide if you haven't got those.

Then you can fit the the neck in the pocket, fit the screws through the holes in the body and use the ends to mark the hole positions on the neck. For the holes in the neck, you'll need a drill bit the same width as the screw body, discounting the thread. You'll need to measure the amount of screw left protruding from the body (not forgetting to fit the neck plate when measuring) and drill to that depth, no more.

To drill the ground wire hole, you'll need a 300mm long drill bit as you'll need to drill at a very shallow angle and you'll need the drill chuck out of the way. I'd suggest a 4mm drill. First mark out the bridge position and the mounting screw positions, so you know the area where the hole need to go, avoiding any screw holes. Then drill a short vertical hole which you can then position the tip of the long drill in to stop it from skidding off the surface due to the shallow angle.

Definitely mask off the top to minimise any finish-damaging slips. You'll need to work out the correct angle to drill at, and mark a line on the masking tape that the drill path will take to get to the control cavity rout (you can drill to the bridge pickup rout if this is shorter/easier, but you'll need to be more accurate as to where the hole comes out a sit will need to be low down to stop the ground wire fouling the pickup cover). Using a wooden block of the right height as a support will help to get the drill angle correct. As long as the hole comes out through the side of the control cavity rout, you'll get a wire in it.