I don't watch all these but are all these mutant shows related / connected to each other or the X-Men films?
Runaways isn't really a mutant team. It's just a group of kids of various backgrounds, whose parents are criminals, which causes them to... run away. They get their powers from various things: one is a witch, one is a gadgeteer, one has some genetically designed link to a dinosaur her parents created, one (well 2) is alien, and one (Molly) happened to be a mutant. A cyborg comes later.
There's no link between this and the X-Men films. There may be a link with the rest of Marvel movies, but it's only been hinted and doesn't really affect plots.