How to Install the OEM EDM F1-Style 4th Brake Light on Your USDM MK5 Supra - YouTube
WAA01 is the one you want. Here's the plug n play harness mentioned in the video:
A90/91 Supra Euro 4th Brake Lights Harness Kit U.S shipping only – I Autowork
You may have rubbing issues on 305/35, depending on how much you want to lower. Although I have different wheels the specs are similar. For your visual reference,
Wheels (Apex ML10RT's):
19x9.5 et 25
19x10.5 et 35
Tires (Continental ECF's):
265/35
295/30
Lowered 0.5" all around on KW...
If you're worried about wind noise, I don't think these small mm gaps are the issue, but you might want to look into wind deflectors. This is a known issue with stock Supras.
Anti-Buffeting Wind Deflectors - Mk5 Toyota Supra | Verus Engineering
Just a heads up, majority of aftermarket parts...
Not sure what your stock exhaust has to do with anything if you bought a new exhaust system.
The valves opening and closing doesn't rely on the car being warm, you control valves with the given controller (should have 2). If you're having issues after using the controller, then I would assume...
1. If you go catless and are worried about something happening to your engine, get an OBD scanner and consistently check every now and then to see if anything pops up. If you want the CEL to go away from being catless, you can tune it out.
2. Yes, it's okay. Most people go catless anyways. If...
If you're stock and wanting to tune, the first thing you should do is an upgraded down pipe. How much power are you looking to push? If you want a considerable power increase there's a list of mods you'd need to do, keep in mind it won't be cheap.
The shop that installed the electronics box for me said that they could do it, but I opted out. Supposedly it can be done but idk anyone that personally has it because Valvetronic isn't too common with Supras from what I've noticed. I would imagine any reputable performance shop could figure it...
I think I know which one you're talking about, I'm 15 minutes from Claremont lol. Might as well take it for a ride so you can experience it, it's free. The experience might change your mind though.