Okay, I was trying to remember if I saw proton torps, and wasn't specifically remembering it, nor any dialogue calling out their use. I'm happy to concede that one.
Likewise, I'd actually made the point when my friend griped about the single squadron thing that maybe a significant portion of the Republic fleet was based on the systems that got blown up in the initial round. I agree, whether that's the case, or whether the Republic is fearful of openly opposing the First Order, it's poorly explained on-screen. Maybe this is something where we'll get more detail in a novelization or something.
The cheers were definitely there in our theater, too. It's why I love opening night crowds for Star Wars releases.
On the subject of Rey -- I also suspect she'll be revealed to as Luke's daughter in upcoming films. Or at the very least, connected in some way to the Skywalker legacy. I became convinced of it when she had that strong reaction to Anakin's lightsaber. (Which I, to my great personal satisfaction, called in a verbal aside right before she opened the box -- yay for recognizing the right shape and size of a lightsaber box -- though I didn't expect it to be Anakin's, specifically...) Your position that she may have had lightsaber training before does bring up an interesting theory that I've just now had in reaction, though -- she could, indeed, have been mid-way through training with Luke's batch of new Jedi (and this doesn't require her to be a Skywalker; it can work more generally) when Ben turned and Luke made the decision to vanish. Luke could have decided, in reaction to his failure with Kylo, that he wasn't worthy/ready/responsible enough to train new Jedi, and scattered his former students across the galaxy, using the Force to either wipe their memory or suggest they forget their time with him and training.
That would, actually, solve my issues with her quick non-study of the Force. It would introduce another gripe about the tiredness and contrived nature of amnesia as a plot device for protagonists, but that one is a much smaller magnitude strike against the film.
Speaking of "Ben", I suspect it's my long-standing and heart-felt affection for Obi-Wan (Ewan is the shining light of the prequels, and would be sufficient reason by himself to not discount or banish them from head-canon and recognition even if one were opposed to all else) talking, but the revelation of Kylo Ren's birth name, the name that Han and Leia gave their son, was more gut-wrenching to me than the murder of Han himself.
It might also have been, of course, that I'd been steadily more and more sure that Han was going to die as the film progressed. I mean, it starts with just the seed of "Harrison Ford is ancient, looks like hell, and obviously can't handle the demands of being a primary character in an action franchise anymore", then comes the sad recognition that they're setting him up as Obi-Wan as he shows some respect and admiration of the potential Rey shows as a pilot and begins to take her under his wing. And then, the deal is cinched when he offers a spot on his crew (in a wonderful little moment) that gets turned down with a rationale we all know as an audience won't fly (Rey won't be allowed to return home and fade into obscurity again), while simultaneously recognizing that Han, Chewie, and Rey won't have a future together as a trio of scoundrels.
The Bridge Scene (which I've resolved to refer to it as until spoilers are more welcome in public conversation) also demonstrates, to me, the damage that was done with the choice of characterization for Ren. If he were intimidating and ominous, the invitation for Han to come out there and make the attempt to redeem him could have come across as ruthless calculation by the villain who recognized their mission; by appealing to Han's desire to save his son, Kylo Ren could have been stalling for the time the weapon needed to fire successfully in a clever gambit. Instead, the whiny kid just wanted to air out his daddy issues with a petulant extension of false hope.
More minor, nitpicky, but still deeply held gripes about dialogue choices: At least in the Bridge scene, but I think a couple other places, Han (and Leia, if elsewhere) talks about there being "light" still in their son. Wrong! There is a light side of the Force, but the proper and established Star Wars lexicon for discussing redeemability of individuals is whether there is still "good" in them.
And finally, to end my reply on a good note -- I agree, Poe was fantastic. I rolled my eyes at his continuous-shot eight-kills in ten seconds performance that stretched my suspension of disbelief at the fight on... whatever the planet with Maz Kanata's establishment was. And he was a little more excitable (in the cheering while flying sense) than I'd expect a storied veteran ace to be. But the swagger with which he comported himself was really great, and he had good lines and interactions with the rest of the cast. He reminds me in some senses of Han, as you say, but I think he's the new improved Wedge, with more screentime. And I'm okay with that, if so (aside from, as I noted above, my disappointment that Wedge isn't a grizzled wing commander or admiral in the briefing or war room).