I’m an Aussie about to go on a road trip from Grand Canyon to Yellowstone in a hire car. What road rules are there that I may not be aware of?

Also, I’ve noticed that if you are turning right at traffic lights, people have been turning on the red light providing it is safe to do so. Is this the case for all traffic lights?

EDIT: thank you very much everyone for taking the time to help this Aussie tourist navigate your roads! I haven’t been able to get to everyone for sharing advice but I have read all comments and your comments are very much appreciated. I’m heading off to the Grand Canyon today and I’m looking forward to seeing more of your beautiful country!