Welcome, randod. Enjoy your stay at GTP.
Manual just takes practice until you develop an ear for it. I find it much easier to drive, because I don't need to second-guess what the trans is going to do.
The little red number is just the suggested gear for the next corner. It blinks when you hit the recommended braking point, which is when you should begin to slow and downshift. It's just a guide and is not always 100% correct.
I usually upshift when the upshift light comes on, but that varies by car. In a Skyline you probably will do better shifting at least 500 rpm below that. Some cars do better up high - I've actually run entire laps of Apricot Hill with the upshift light blinking, in a 1100-hp Viper GTS with the race transmission. You just need to pay attention to whether the car is still accelerating or not. But you definitely want to avoid the rev limiter (typically a few hundred rpms above the redline), because that will slow you down by cutting fuel to the engine.