There is no R34 in the game that I am aware of. All of the vehicles in the game are purpose built race cars. Here is a list of cars
http://www.iracing.com/cars/
You cannot upgrade the cars.
The cars can very much be tuned, as long as the series you are racing in allows it. For example, the Rookie Global Mazda Series does not allow tuning of any kind. If you participate in other racing leagues, (for example, I race in the Precision Race League) tuning is allowed and very much necessary. There really isn't anything on the car you cannot adjust. The Ferrari GTE car that I am currently racing can be adjusted from the number of clutch plates, to individual tire pressure, camber, toe, ARB, rear wing, you name it.
I believe cars are running $11.95 each and tracks are at $14.95 each but you can check the website to verify. This is outside of the cars and tracks you get free with the monthly subscription. There is a discount for bulk packages. While it seems expensive, it is absolutely worth it.