I'm not familiar with the wood, but the web says that cottonwood pores are almost microscopic in size, so they shouldn't be an issue and need grain filling as such. If the surface of the wood feels smooth, then I wouldn't bother. But it it feels uneven like ash does, and you think it's something that sanding won't fix, then a neutral grain filler might be needed. But I don't think other kit builders using this body wood have grain filled to date.

The finish should fill those small holes, but I haven't used that oil, so I don't know how well it will fill, Could be worth having a go on just those areas first to see how many applications you may need to fill them. I tend to try and fill small gaps with the finish, Anything larger and I use a standard DIY store fine interior filler mixed with some cheap artists acrylic paints to match the wood colour as best as possible, applied with the end of a cocktail stick. The striping does make it harder!

Holes don't need to be protected from finish. The only time they may need to be protected is if you do any wet sanding of the finish before polishing, when it's a good idea to fill them with wax to stop the water soaking the wood, expanding it and cracking the finish. Putting any wax on before the finish may prevent the finish from adhering.

The holes may need to be cleared out before wires or screws are fitted, but that's an easy job to do with a bit of stiff wire.

If you are going to shield the cavities, then the underside of the pickguard (at least that part over the control and pickup cavity area) will need to be shielded as well to create a Faraday cage to make the shielding worthwhile. So some of that pickguard will need to be sprayed with the conductive paint.

A P-bass pickup is humbucking, one of the two sections is RWRP to the other, so not shielding the bass is an option if you use a clear pickguard. You are unlikely to pick up much noise at all in the control cavity, except in a really 'hostile' electronic noise environment e.g florescent lights, dimmer switches, large transformers etc. So if you go down the clear pickguard road, you may want to leave the shielding to start with and see how you go. Of course your wiring will be on display, so you'll need that to be as neat as possible.