RNG, in a sense. Skills mostly come from passives, you need to subject Karryn to more than a few, for example, handjobs to earn the passive that unlocks the ability for Karryn to initiate a handjob without praying to the inmate RNG. Slut levels contribute nothing to skill acquisition.
"Extra actions when knocked down" would be...well - getting knocked down some more. Passives are also random in the sense that some of them are "do X action Y number of times" whilst others are "do X action Y number of times with different partners", i.e. some can be grinded in one battle using the same enemy whilst others require different enemies for it to count.
The only "extra action" specifically related to being knocked down is "Fallen Rest", though, which lets Karryn regain some stamina without getting up. Not much to gain from that specific passive.