My Sigma 150 runs pretty cool most of the time 70-80°C on the road with radtec radiator. Only gets hot on track / in traffic. Fan also comes on around the 100°C mark. My gauge matches up to Easimap. You could try a 89°C stat or similar if you use it mostly on the road and see if that's better.
I take it you mean the Titan LSD rather than the diff? Seeing as Titan recommend a rebuild every 10,000 road miles, I seriously doubt changing it a lot will bring longevity.
#9 4x rivnuts are more than enough for a 1kg battery. The Caterham tillet seat brackets (fixed) are also rivnut and that secures significantly more weight...
Log the lambda on a graph and see if it's switching voltage smoothly and regularly. I wouldn't be too worried about a sooty exhaust, I'd just take a spark plug out and see what the colour was to see how the engine is running.
It's the other way around. The lambda won't be used until the car is warm enough. You'll see on Easimap it says something like lambda waiting for coolant temp.