So, I had purchased an IMAX ticket prior to seeing the movie, and I didn't want to waste the money, so I went anyway. All I can say is that if you see it in a dome theater, you better be prepared to get there EARLY. You pretty much need to either be at the top or be prepared for some neck strain. There were also a crap ton of people lined up as I left.
Anyway, getting to see it again let me look out for some points that we've been talking about.
So, I think it's pretty clear that The Knights of Ren destroyed the new Jedi Order. Han specifically uses the word "destroy", and in the flashback sequence, you see Kylo stab his lightsaber through a person that appears to be wearing of those dome-shaped Jedi helmets.
That Stormtrooper with the melee weapon was the only one that I saw that had one. So, I doubt that most Stormtroopers receive training in melee weapons.
Kylo Ren was most definitely trained by Supreme Commander Snoke. When discussing the awakening, Kylo Ren states that the grace of [Snoke's] training allows him to resist the call. Plus, Snoke said that he's going to complete the training. Usually, you don't say that you're going to complete something if you haven't started it already.
The Starkiller, as one would assume by its name, does appear to destroy the star that it drains. Finn states something like "the star goes dark then disappears", which you'd assume means that it's gone. Although, where does the First Order keep getting stars from if that's the case? Also, the first time when they fired it... it was daytime. Did they already drain a star? ...or are/were there more stars originally.