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So...why, exactly, doesn't Ten hand over the Monk's information to Eight? (Not saying what the information is, on account of spoilers.)
The Time War is a fixed point in time?
Actually, it is specifically stated that, as a result of everything else that's happened, the entire universe is currently in flux. I think Ten just did (or rather, didn't) do it in order to preserve his own personal history. Which I personlly think was a bit of a dick move.
He turned around and saw Nine and Rose standing off to the side before making his decision. Yeah, it was about his personal history.
We're talking about meddling with history here.
The universe had just healed itself after all the shenanigans in this story. To undo the Time War would mean undoing one of the BIGGEST things to ever happen to the time stream. Who knows what kind of effects undoing it would have.
Why does Eight remember he's the Eighth Doctor, but not how Five used to look?
It was the Guardians. They played with Eight's memories, they made things hazy for Nine and Ten, and they kept the Time Lords in Eight's time streamnote aside from Maxil, who recognized Six from recognizing the other incarnations of the Doctor (which they should have been able to do regardless of the Doctor's incarnation, since Time Lords don't base recognition solely on outward appearances).
So...how DOES Maxil recognize Six?
The Valeyard flat-out tells Maxil that it's the Doctor. The Renegade Daleks obey only "the Keeper" (aka the Valeyard), and they've confused Six for the Valeyard due to similar psionic levels, so naturally the Valeyard doesn't want the Doctor meddling in his plans. Chilling when you consider that the Valeyard is the only one who recognizes the other incarnations, while Eight can't.
It's also worth noting that Drax easily recognizes Nine when they first meet. How he is able to do so is anyone's guess.
Shouldn't the Doctors have remembered that for future incarnations?
The First Doctor explains it in detail on this page. The short version is, thanks to the Timey-Wimey Ball and the Guardians' unnatural interference, the Doctors' memories will return to their proper states of being once they reenter their own time streams. TechnobabbleHand Wave, basically. (That said, it's likely it won't affect Ten, since they're all in his time stream.)
Why didn't the Guardians just grab Ten, sit him down, and make him make a decision? Why bring the other 9 Doctors in at all, if they really only needed the one? Hell, I love this story, and think it's great, but really, there was no need for them to make their little game so complicated when you think about it.
It's their nature. Both Guardians are Chessmasters, and for eons they've been playing a game against each other—Order versus Chaos. The only constant in foiling either of their machinations was the Doctor, who successfully countered the chaotic Master and the ordered Daleks. Over time, both Guardians came to the conclusion that the Doctor didn't represent chaos or order—he consistently maintained a balance, even more so after the Time War with the instability of the universe. This was unacceptable to the Guardians, so they plucked the Doctors out of their timelines in order to place the universe back into flux and force a conclusion—and the Doctors still fixed everything and maintained a balance. So the Guardians lost patience, captured Ten, and pretty much forced him to choose since he was the only person who conceivably could. Naturally, the Doctor Took a Third Option, thanks to Nine's machinations.
What about the eleven forgotten companions? Why didn't they feature at all?
Because there were already more than enough characters, and the author probably just couldn't figure out how to fit all of them in.