You can advance straight onto 3-D graphics if you wanted so long as you have sufficient knowledge of 3-dimensional space. The same applies to 2-D graphics: if you have the know-how, you can advance. Besides, Disch wrote an article which states that the console is best avoided as a platform for games.
Game programing is very math heavy, in fact I would say you need more Math experience than you need programming experience. The programming is the easy part ;)
Yes, start now, but expect to get caught up often, it isn't easy. When you do get caught up then ASK, don't just give up.
Learning classes will help to organize things in a helpful way, pointers get interesting when you start using them inside of classes, and some graphics libraries are heavily dependent on structures (Windows API for example).
Basically get started, but don't stop going through the documentations and tutorials for native C++, they will continue to build up you knowledge and abilities.