1) Which XBox controller are you talking about? 360 Wired, 360 Wireless, One, One Elite, etc. I can only speak for the XBox 360 Wireless controller config. 2) For the default config for the XBox 360 controller, Start, LT (Brake), RT (Gas), A (OK), B (Cancel), and Y (Rear View) buttons should be able to do something. 3) The tutorial before every game is more of a demo video, and less of an active tutorial. You hit the Gas button/trigger to advance through the screens, and you hold Start to skip.
I know it's a really late reply, but I hope this helps.
I am using the 360 Wired one. I know it is more of a instructional video, it would not accept the button needed to continue (Gas\RT). I was able to pass by using the keyboard. After that playing the laps was fine.