Just saw it today. All in all I liked it.
The "big guy" isn't necessarily big -- it's a hologram and Palpatine used a giant projection when he talked to Vader in ESB, so it's probably part of the standard Sith protocol for use in cowing underlings.
While it initially looks like the Empire/FO got stuck on building super weapons with major weaknesses, that's actually only really true for the first one in ANH. The second death star wasn't finished, once the rebels knocked the shields down (which only happened because the Emperor was overconfident and let the strike team onto the forest moon as part of his trap) they actually flew INSIDE it and shot torpedoes into the main reactor. Hit the reactor and you get a big explosion is pretty much a standard trope for SF of any kind. For the Star Killer, the X-wings were ineffective against it until Han & Chewie's bombs blew a hole in the armor for them to shoot through, and then they blew up the "resonator" (the magic thingey that held all the power from the sun, so effectively the same as the reactor).
The real question in the blow-up-the-superweapon plot is why only the Millennium Falcon can fly through a shield in hyperdrive, and why they couldn't just fly the X-wings in the same way? OTOH, we've consistently seen it do things that make no sense (it's a freighter, even if Han has hopped it up how does it outmaneuver dedicated one-man space superiority fighters?), so perhaps we just have to accept that it's a magic ship.
The guy who was buying the scrap on Jakku was the "owner" of the Falcon, it wasn't abandoned. Rey says it hasn't flown in years, but that doesn't mean the scrap dealer (whose name I've forgotten) wasn't keeping it up. Maybe that's why he was buying all the scrap? :)
Rey being able to open any door on the ship by manipulating fuses the size of a fist doesn't make a lot of sense, but then neither did the fact that in ep 4-6 everyone leaves computer ports hanging open for passing droids to plug into and do whatever they want to the computer system. I mean, seriously, hasn't anyone in that universe heard of network security?
And yeah, I get the impression that what happened is that the Rebellion turned into the Republic and split the territory of the former Empire between them and the FO, while the Resistance is in effect, a "new rebellion" inside the FO territory. Gotta remember that they threw out all of the canon from everything post-RotJ, so the idea that the Empire collapsed after Palpatine's death and was quickly replaced by the Republic isn't necessarily still valid.
I have to say, though, at the end it's a good thing Rey and Finn were fighting Darth Emo (as I've heard him called), rather than Vader. Vader would have mopped the floor with them.
