One of the most famous drag racers in history was a woman, Shirley Muldowney.
Angelle is a 3 time record setting bike champion. Karen Stoffer is another bike rider that is winning. There is at least 1 woman competing in the top fuel dragster class right now and many, more in the sportsman classes. John Force's daughter is doing real well in alcohol dragsters. I don't know about elsewhere, but women are a big part of drag racing in the US and I love it.
As for the photography, for your weekly local races, I don't expect you'd have much of a problem. For special meets put on by a promoter, I would get permission from them, they will usually want some pics in return.
I work for one promoted event now (6 races) and have had another photog that showed up, lied to get access to the starting line, then put pics up online, with the event name and everything as if he was "official". On top of that he totally copied the website of a fairly well known drag race photographer. The promoters were very upset and will not give him access again. I know I lost some sales after I put a lot of time and effort into my website and advertising. It's not much different than going to a wedding, taking pics, handing out cards then posting them for sale as if you were the official photog of the wedding. I only mention this because you should make sure you aren't stepping on toes at an event such as this. A small locally promoted drag racing event only has a certain amount of business to go around.
As you get to bigger events, you will find it much more difficult to get access. As Daniel said, NHRA events are the most strict of all of them.
BTW, I don't sell pics at the event, I looked into it but my events just aren't big enough for it, plus I'd rather concentrate on my photography and not worry about getting files uploaded and printed. I post them online on my site and use paypal for payments or they can mail me a check. Add enough shipping & handling to cover shipping, envelopes and labels and you're set. You can see it here: www.gulfimagesphoto.com/txshootout
For my cards, I just made a little collage in 4x6 and had a bunch printed at Walmart. They even made me a cheaper deal for buying a quantity. My wife goes through the pits and hands them out.
Cheers,
Bobby