What I would do is go to the left or right side and loosen the corner. Get a carpet pull and give it a few whacks to pull it tight. Because I cant see either side, I would suggest if possible you get a carpet transition strip.

There are 4 general types:

https://brandon-lighting.com/methods-of-dimming/

The only ime I've seen a variable resistor in real life is in a car. It was for the high medium and low select on a fan speed for heater and a/c. I doubt they would have used them in a house because it would be dangerous due to the heat it creates but who knows.

I'm no electrician but that's not correct. First, what gauge wiring is ran to the lights. Second what average fuse is the line ran off of. Third, is there anything else sharing the lights with that fuse?

Those questions aside many companies recommend a max number of lights per switch. For example, verilight says 10 led lights max.

I mentioned some things you didn't ask about because I was unclear who ran the electrical. And your knowledge about what's on the fuse they may share.

"NEW" Dimmer switches CONTROL THE WAVE FORM, they have nothing to do with amps or voltage directly.

So even if you can control 10 lights on 1 dimmer - it doesn't mean you should. You need to do your research and answer the things I mentioned in the first paragraph.

This may determine while the dimmer switch can control 10 lights, but electrical line or fuse may only handle 3.

That's tough- see if you can get some powdered graphite..same as baby powder but works slightly better. I'm aware of it from my own research but have not tried it

Shim it from underneath. I've a 105yo home and it's worked every time

You don't have experience with plaster and lathing do you? And you don't put joint comping on lathing. Lathing is flexible..plaster is 10x harder..and the irregular borders would need be screwed down..it will never hold. He need to cut the loose stuff out and replace with sheet rock

Your better off getting half a sheet of sheet rock. Maybe a 2x4 as a nailer. While you could scre the hell out of that and re-plaster it will never come out as nice or as easy as replacing it with sheetrock. My whole home is plaster and lathing..I hate the crap! Use a sheetroch knife to remove anything loose and even up the edges. Depending on where the studs land you may need a 2x4 or some kind of wood nailer for the sheet rock. Plaster is cheap and cures very hard. You may find it easier to just use modern mud aka joint compound and tape

Cut a piece of the rubber out and super glue it. Just a small dot of glue.