I caught myself doing that same "gangsta lean" bit my first autocross. I couldn't see your right hand, but if it was like my first time, it was resting on or near the gear shift.
I also remember thinking that that sea of orange cones looked like my son had thrown all his toys on the living room floor. Sure, they tell you what each element means and what you are supposed to do with it, but it's a lot like learning a foreign language.
My recommendations for new autocrossers differ (slightly) from what's been said.
Looking ahead is essential, but I don't push that too hard until after they learn to "speak cone". The gibberish "ahead" looks a lot like the gibberish that's right right in front their hood. I recommend they not drive faster than they can see. (meaning see and decipher) If you get on the gas before you know where you want to go, you will go nowhere fast.
If they are disciplined enough to not get ahead of their eyes, their desire to go faster will naturally get their eyes further ahead. (it just takes some time)
I have the same philosophy with hands and the steering wheel. I tell students that hand-over-hand is generally wasted energy, but not to "sweat" it at first. (at least not beyond just using both hands.)
As they get familiar/comfortable with the cones, and their eyes start getting further down course, the hands start to end up where they need to be in anticipation of "what's next." (with only minor reminders)
Good tires tend to cover up mistakes. As a new driver, you want to know every time you make little mistakes. Crappy tires are often good for that. I recommend killing whatever tires you have on there now and learn as much as you can with them.
The GoPro Santa brought me is great for catching hands: