The tragedy of Mao Zedong is that he started out with such idealism and benevolent intentions. He fought to free his people from oppression, both by the brutal Nationalist government and by the Japanese invaders, and he succeeded. He envisioned creating a utopia where everyone was free and equal, where everyone took responsibility for their own behavior and their own morality and everyone worked together to keep society working smoothly. And when he started out, he understood that it was supposed to be a long-term process, one that would take generations to unfold. Marxist theory was that a civilization had to go through numerous stages before finally achieving true stateless communism. (In practice, we've never actually had a communist society, since all the nations run by so-called Communist parties have stalled at the socialist-dictatorship phase, since of course the fatal flaw in Marxist theory is that it naively assumes an authoritarian state can be trusted to bring about its own dissolution.)
But the problem was, he got older. He became aware of his mortality, and got impatient to see his goals achieved within his lifetime, so he tried to force China to go through the evolutionary stages faster with the Great Leap Forward, and in so doing he inflicted horrible atrocities on the country and betrayed just about everything he'd originally stood for.
So maybe the Doctor knew Mao at an earlier point in his life, when he was still an idealist and a liberator. And thus he knew that there were qualities to admire in the man, and reasons to take pride in having known him. The thing about history is, there are few people you can really cubbyhole in the "good" or "evil" column. There are some pretty unambiguous monsters like Hitler or Pol Pot (though even Hitler was kind to animals), and some pretty saintly sorts like Mahatma Gandhi and the Dalai Lama, but most important historical figures are somewhere between the extremes. As a rule, the greater your capacity for good, the greater your capacity for harm as well. Some people, a lot of people, do both over the course of their lives.
I think you can draw a comparison with how the Doctor sees humanity as a whole. He's aware of our darker side, of the great evil and cruelty and hate we're often capable of, and he rarely hesitates to call us on it and chastise us for it. Yet he continues to cherish and admire humanity because of the great goodness and creativity and love we're also capable of. So if he can forgive us as a species despite all our collective atrocities, it stands to reason that he can still see the good in individuals who've done horrible things. And we've seen that he is capable of that kind of forgiveness on the individual level; he stayed friends with the Brigadier despite what the latter did to the Silurians, and stayed friends with Leela even though she kept ignoring his no-killing rule. He's pretty much a hate the sin, love the sinner kind of guy, unless the sinner is a Dalek.
As for the Doctor's age, Moffat's on record as believing that the Doctor doesn't even remember how old he is and just makes up numbers as a convenience. After all, when you travel through time itself, how do you keep track of such things? And which world's calendar do you base the calculation on? The whole business of keeping track of how much subjective time has elapsed since your birth probably seems like a quaint and parochial custom from a Time Lord's perspective. So any old number will do.
It stands to reason, though, that the First Doctor lived a very long time compared to his other incarnations, because he was the only Doctor to "die" of old age. All the others have had their lives cut short because they died from violence, or were forced to regenerate in the Second Doctor's case. And if it's true that Eleven aged 200 years while eluding the prophecy of his death, yet didn't look any older at 1100 than he had at 900, then that suggests something about how slowly Gallifreyans age. Along with the fact that Romana was 139 when we first met her and looked like a woman in her late 20s.
I've always figured the First Doctor lived so much longer because he spent most of his life on Gallifrey. He didn't steal the TARDIS until he was already a grandfather -- although admittedly if you live for centuries, that point could be reached quite early in your lifespan, depending on whether sexual maturation is commensurately slower. And before he met Ian and Barbara, he was evidently less inclined to be heroic or intervene in other people's problems, so he wouldn't have been purposely risking his life as much.