"Mag ik hier zitten?"
Translation:May I sit here?
Does the same thinking apply to ken and mag as it does to can and may in English. Can = ability, may = permission?
Almost. I think you mean "kan" which comes from "kunnen" which means 'to be able to' and 'to be possible,' and it's always used as helping verb together with an infinitive. There's also "kennen" which means to 'be familiar with,' 'to differentiate' and 'to recognize.' So in Dutch it would be "Kan ik hier zitten?" instead of "Ken ik hier zitten?" Mag (from Mogen) does indeed mean 'to be allowed to.'