The autocross cone scuffs will usually polish off as they are pretty light scratches. When it is scraped bad, it can be pretty bad and permanent damage. On my previous car, I spun at the end of the course and hit the timing camera which left a dent on my rear door.
I had to use paintless dent removal to take it out.
Using clear bra does help avoid permanent damage but I find the clear bra itself gets damaged by the cones and sometimes is harder to clean than paint scrapes. At least with clear bra you won't end up with permanent damage.
The best thing is to avoid the cones. If you are finding you are spinning and hitting cones pretty regularly, you may need to dial it back a bit or have an instructor or experienced autocrosser ride with you.
As for track, you will get melted brake and tire material get stuck to the paint. It comes off with tar remover.