No need for special or additional insurance, and you do not need any special equipment. That is why autocross is so fun, accessible and inexpensive.
Generally autocross
is on a flat open lot, and defined by traffic cones. But sometimes you need to be creative or have the option to introduce other variables, in this case the banked portion of a track. Which sounds really fun to me actually!
You do not need the rollbar extender, fire-extinguisher or racing seats with the 5 point harness. Just bring your car, and an open mind! You might want to get your own helmet eventually, though most clubs have loaner helmets available for those just starting out.
Do it! Get out there and give it a try!