You crack me up, dabo, awesome recap.
You left out only a few things.
First, Claudia and CJ speak to each other in another language at first, but after a few sentences they decide to speak English. Jacob and Claude grow up speaking English, which explains Jacob's American accent.
CJ swaddles the nameless baby in black, because she only had enough white swaddling for Jacob. They are fraternal twins and one is born blonde and the other black haired.
As far as we were shown, neither kid ever asked if they had a dad, or even knew about fathers. Finally some LOST characters with no overt father issues. Instead they have crazy mom killed real mom issues and Mom likes you best sibling issues. They are kind of like Tom and Dicky Smothers that way.
Claude builds the donkey wheel, and he explains how the light hits something and that's why the wheel turning takes people off the island. So now we know.
Claudia and the boys live in the Caves and in case we didn't figure out that they are Adam and Eve from "White Rabbit" -- we see flashbacks of Kate, Jack, and Locke. What I notice most is that Kate's hair looked very just out of the salon and her face was made up and not dirty like it is in Season Six.
The cave that Jacob throws Claude into is where the light is that is the spirit in all of us, and is different than the cave where they all live, the one where Jack and Charlie were buried alive. The cave of the light, I am going to guess that the pool of the Temple was fed by the spring, and that the Temple got built over that spot. At this point I'm not sure they'll ever say that but that's my story and I'm sticking to it.
The place where CJ bashed MIB's head against the rock where he invented the wheel (even though I'm not so sure these people had invented the wheel) -- becomes the Orchid.
Of course, Claudia washed up on the exact same beach were the 815 survivors camped all that time. We don't know why she was on a boat or raft as she seemed to be one of the bad people who live on the other side of the island, but I'm guessing that the primeval shark that will eternally swim with the DHARMA logo busted up her vessel.
The only thing we found out about the Rules is that CJ caught her boys fighting and made some rules that they can never hurt each other. Claude told Jacob he couldn't hurt him because of the Rules that Mom Said, but Jacob jumped on him, beat the crap out of him, and threw him into the stream that took him into the cave where the light was, and the smoke monster came out one way and his dead body floated out the other.
Which leaves me pretty confused about Mom's rules because I'm pretty sure that Jacob hurt his brother in a very Cain and Abel reminiscent BAD way. So Jacob is the Cain character, which is not a nice thing to be.
CJ gave him some wine to drink and now he is the caretaker and will probably not age and will inherit the ability to make Richard Alpert immortal, but that wasn't explained.
Claude as it turns out was the "special" one and Jacob was Mom's second choice, but he did weave a nice tapestry.
Do not ask how he ends up living in a giant statue of Tarawet by the sea.