These are all correct. We also use the verb 'to brake', a lot, as Jordan has used it.
I would say 'I had to brake suddenly', or 'I braked slowly to avoid skidding', or "Brake!! Brake!!' (to a learner driver). 'Apply the brakes' (or its opposite, 'release the brake') is the sort of thing you read in an instruction manual.
Pumping the brakes means putting your foot on and off the brakes quickly, to dry them or to avoid skidding.