Rachel will probably remain factionless (though still definitely on the 'good' side). I mean, she knows a lot of characters on the Dinotrain, so she might end up hanging out with them a bit at some point, but...even then, she could and probably would just leave if she didn't agree with something they're planning on doing. Or if they get too bogged down in making a decision on what to do.
Not sure what's going to happen with Mio. I know at the very least, she's not going to join Dai-Black Cross (or any other villainous groups), but other than that, it really depends on how things play out.
And I think people are meant to get their powers once all the introductory stuff's done, everyone's in the museum and the attack starts/is about to start.