I've an issue. When I start a race, my car moves forward when lights are yet reds without I have pressed any pedals. Why?
This is actually more common than we may realize. I've seen this same issue in other titles as well. It doesn't have to be a starting line that has slope, either. Sometimes, the car just creeps forward a bit when gear is engaged. The obvious trick is to hold the brake pedal down until the lights go green / off. Easier said than done when we have 3 pedals and only 2 feet but, using heel & toe technique can help.
There are new settings in the current UI to automatically start a race with the brake automatically set. Under the difficulty tab, auto hold the brakes, turn on the lights, engage the clutch, even(horrors) start the engine automatically. These are all things that are easily accomplished just by being ready at the start of a race and depressing the brake & clutch pedals. But those relatively new options are there for ya.
Check your throttle pedal isn't having issues - check its range and operation. In the rF2 calibration screen you can press "Set Min" under the throttle graph without pressing the pedal to reset the low point, and you can even do the same with a very small press of the pedal (then press set min) to give some deadzone.