@Bartimaeus should get a medal for persevering until the end! Congrats!
As for the movies, they did a lot to explain what was going on in the originals as far as the story goes, as far as the characters go it was mostly a rehash of the originals (minus she who shall not be named), although this time around he gave us some closure and didn't blueball the ending. Overall I much prefer this ending to what we got with NG:E, I would even go so far to say that I like it very much.
I think it goes back to what KP was saying, these movies are made for the people who already watched the original series and so a lot of the character interactions have been skipped or have simply been sped through. Overall the focus was more on the "story" this time around.
As for what the story is, this is how I understood it. The rebuild is the continuation of the original series. At some point after the ending of NG:E someone wished for a restart of the world, it's also hinted that this restart may have happened a couple of times with different variations of reality, ie. wishes being made that affect the world. Gendo's wish being that all barriers are removed and thus all beings become one (this was a theme in the original series too) so he can be with his wife again who is now part of the original Eva (and after the second movie part of Shinji?), so he tricked pretty much everyone from the beginning to make this scenario happen. Now to make this happen he needed the spears, ie. wishes. That is why he needed the impacts to happen as they provided the materials for the spears, ie. fuel for the wishes. The rest is I think pretty clear by the end of the last movie, Shinji mans up confronts his father and with the last spear wishes for the end of Eva and thus choosing to grow up and face the world on his own.
As for the ending itself I think it's a comment on the real world being interesting enough without Giant robot battles and magic technology.