I've not tested it, but I'm going to say no. The rail the camper top uses sits on the side of the bed. The bedrack sits in the same spot, so you can't have both.
Do a chalk test to see what pressure works for your setup. I'm running 25 psi on 35x12.5x17s. I was running 35 on the stock tires for a (gasser) sport maxtow. I'd imagine yours is somewhere in-between.
I don't have issues with mine, but I started with the Halogen lights. Since it sounds like it's a low voltage issue, I'd try getting a tuner (Tazer/Jscan) and changing the vehicle over to thinking it has Halogen fog lights.
IIRC, there's someone on this forum that found a copy of the controller Genesis uses for much cheaper and mounted a battery on the frame under the bed.
TrailRecon also did a build where they had a box attached to their bedrack that housed the battery, controller, etc.
If you find a location for a second battery, you can still do it yourself for cheap. I can't claim to know why the Genesis is so expensive, but the extra technology in it as well as the design time to make it a nice clean install will definitely raise the price up above buying a generic switch...
You can wire in a second battery, though under-hood space is a little tight. There's also systems like the Genesis Dual Battery setup that have a smart cutoff to try and save your cranking battery, but also have an override button to link the two together if you need it.
Trim piece for the soft top above the doors has it in. I'll see if I find the exact spot in the morning and take a picture, but I've seen mine partially out a couple times.
Edit: For more location info, front and back of the door frame, outside facing. The two little brackets are connected...
As far as I can tell, it'll attach to the OEM trail-rail. I've got l-track in since it was cheaper, so that's not something I can test.
You do clamp a rail-esque system down that the bows slide into, and that's needed for the tonneau cover, so maybe that's where the miscommunication happened.
I don't see how. The entire thing is contained on a clamp on rectangle and is more or less symmetric when up. Unless enough air can get in through the removable window to make it a giant parachute, I don't think any damage could happen.
The side panels wouldn't be rainproof anymore, since...
Quadratec also sells a harness that'll have a connector for both DRL and running lights.
https://www.quadratec.com/p/quadratec/daytime-running-lamp-adapter-wiring-harness-jeep-wrangler-jl
They're all on the same frequency, they just transmit a different series of codes. It's possible, though extremely unlikely that you'll transmit within the range of the accepted codes for another person's FOB. If they used all symbols on a standard keyboard as part of the code and transmitted...