You can, however, put whatever amount you want (up to the small claims limit) in the initial paperwork. It would get reduced to actual damages if you won. But...big companies often try to settle with you before the actual court appearance. By padding it, you set an expectation that might help. They are likely to settle if the amount is less than the cost to have someone appear.

Sort of / not really.

I guess treble damages are not called "punitive" but they're also not "actual".

https://en.wikipedia.org/wiki/Treble_damages