You must remain on the named roads. From experience, I can tell you that one honest mistake, a wrong turn, can land you in the big house. Its pretty ugly....dont get stuck somewhere you don't belong.
Do not. It is a terrible idea. That would be vehicle abuse, also some of those paths are not marked and no gps or cell service can get to them so if you get lost you are SOL
There are many dirt roads in the park so stick to them
Check in at the office near your site. They will tell you where you can be...with your ATVs
After you register with the office there are some places you can drive your vehicle but it's more for hiking trails
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