Thanks for your input guys. I researched a bit and read that a complete 365 gearbox costs around 4 - 5 k € here in Europe and that's the same ball park as my new diff. With the new diff, I have no risk of used parts, which may be damaged without me or even the seller knowing. That's why I prefer the new parts, even if the 365 gearbox could save me a few Euros.
Regarding the wheels, I'm already at the absolute limit of my race series' rules. I went from Kumho tyres (235/45R13) to Pirelli (225/45R13) and the Pirellis have the smallest allowable diameter. That reduced my top speed from 236 to 232 kph. Even if it would be legal, I'm not even sure, if there are 13" semi-slick tyres available, which fit on my 9" wide rims and have a smaller diameter compared to the Pirellis.