Yes, the outer braid can either be used as a ground path, and connected at both ends e.g. from pot back to pot back, or it can be used simply as a shield and grounded at one end only. Whilst it generally doesn't matter on a guitar, it's not a good idea in principle to create a closed loop of ground connections as it can be a bit noisier, and with longer runs 'ground loops' can pick up a lot of noise due to divergent ground paths with different resistances.

For the pots, I'd think about getting some better quality replacement ones, either CTS, Bourns or Alpha. The volume pots should definitely be audio/log taper, and whilst tone can be audio(A) or linear(B), I much prefer audio/log taper for tone as well as the control action is more spread out and not bunched-up near the bottom end of the pot's rotation. You'll want pots with medium length shafts.

Whilst you can fit everything through a pickup hole, which is a lot easier than fitting the harness through an F-hole, it's still not the easiest job to replace a pot, so I'd fit good quality ones to start with. I'd go for full-sized pots rather than mini ones as well; definitely easier to solder to the back of a large pot than a small one.

If you stick with the kit pots, then my choice would be to use the two (A) pots for the pickup volumes and the (B) pots for the master volume and tone. I doubt I'd ever use the master volume, and there's no difference between A and B types when turned up fully. I normally don't touch the tone knob either, so whilst I pick the tone controls for what I think is best controllability, I rarely use them!