[4RE KLR]

Well anything is possible I suppose. I would not recommend mixing the two types of wiring. Yes it was probably done by someone who did not or could not get to the room in question.

If you can get to it to pull all the wires new in Romex I would recommend mounting a sub panel somewhere upstairs and run one large wire from the main panel to the sub panel and then wire the room from the sub panel.

You need insulation in the Attic. What I see and hear in this business never seems to amaze me. You need insulation under the floor that is why the kitchen floor is cold. That will fix that problem. Yes you can do it yourself. Get a damn good respiratior, a good pair of gloves and some enclosed goggles first. Remember you will be looking up at it while trying to staple it in place.

Sounds like you could do most or even all of this. It does not surprise me that there is no ground. The old homes are famous for that. The polarity is an easy fix. I would fix the ground problems FIRST!

If you run a new sub panel you can update to newer more readily available panels and breakers. I would recommend you do not throw away the old breakers. You could need them in the future for replacements.