I'm at what appears to be the end of the game, we're assaulting Comstock's ship, and I'm enjoying the game, it's just that I literally have no idea what's going on.

Is the whole thing with old lady Elizabeth and ruined future New York supposed to be what MIGHT happen if Booker doesn't succeed in getting her out of Columbia? What sort of stock do the english couple have? I think I get how they became trans-dimensional beings and all, and I've gathered that they're twins, and that they seem to be in a romantic relationship, although I'm not sure if that has any bearing on the plot.

Will I get it by the end of the game?

Don't think about what 'can' happen. What you saw in New York has happened to one version of Elizabeth. She's given you the note to stop that happening to another version of Elizabeth. There are multiple universes and everything that you see has happened in at least one universe.
As for 'your' Elizabeth...well, which one is yours? Maybe that old one is her. Maybe that's what will happen to her. Maybe it won't. The point is that it definitely happened to at least one Elizabeth. It definitely happened in one universe. It may or may not in yours (although you've already been through like four universes so far, so which one is 'yours' is impossible to distinguish) if it isn't already your universe.

As for the couple, they're not twins, they're the same person from different universes. One of them was born a male, one a female. They refer to each other as brother and sister because referring to each other as transdimensional =-doppelganger-slash-universal-equivalent is a bit of a mouthful. If you think they've got some weird romance going, nah, it doesn't really affect the plot, really.

I...have no idea how they conveyed that in the game.

Thanks though. That helps a bit here.

A couple of questions:

1. Is it confirmed that Anna's birth was before the baptism? What evidence is there to suggest this? I think it makes a lot more sense if the baptism occurred beforehand rather then after.

2. Does anyone know or remember how Booker died in the universe where he is fighting alongside the Vox Populi?

@laigerzero: Anna's birth was after the baptism. Booker explains he was baptised immediately after Wounded Knee (which was in 1890) and Anna's birth is approximately 1893. I don't believe details of Booker's death are explained, but the way characters treat his 'return', it was clearly confirmed.

This thread

has all the answers you seek.