Mumkin, as I understand it, Literally means "possible".
But, if you think about it, that can be used to mean "maybe". Like if I ask if you can do something, and you answer, "possible", that means the same as saying "maybe".
It also can mean "May I", in that it can be phrased as a question just by making it sound like one. So you are kind of saying "Is it possible that I can..." etc.
Or you can use it to literally mean "possible". Someone asks if you can do something, and you say "Mish mumkin" or "Not possible".
So, yeah, it means ALL of the things listed above, depending on how its used.