By the way, we have no indication that the Starkiller base ever moves. Why would it travel through hyperspace if its beam can instead?

Here’s the other thing about the base, just because it got destroyed doesn’t mean that the First Order is done. In TLJ we see their fleet, why would any of those star destroyers be on the base? Of course they wouldn’t have been destroyed. And we know that Snoke isn’t there, so the information that he has his base of operations on a mega star destroyer isn’t a terrible surprise.

And the thing about the FO in general, is yeah, we don’t have any idea how they became so powerful - in the movies at least. I don’t see that as a problem, it’s not a plot hole, you might wish that they had explained it but it’s not something that’s unexplainable. And there is something of an explanation in the new canon content. As to whether the FO is a “fringe” group, well that depends on your definition of fringe. I don’t think there was any question in TFA that the FO was powerful and resourceful. TLJ doesn’t betray their galactic standing.