Specific requirements tend to vary from track to track. I suggest you find the website of your local track and see what they say. I know at California Speedway in Fontana you don't need a helmet unless your car runs faster than 14.00 but at Qualcomm Stadium in San Diego you need a helmet - period.

You usually don't get into the roll bars, harnesses, etc unless you've got a highly modified or stupid fast car - like 10 second range.