Altaïr's lengthy rant into the nature of religion seems to be the game lecturing the player about the irrationality of it all and how death ends life forever. This, despite the fact that All Myths Are True and a form of scientific reincarnation exists with genetic memory. It's quite likely that other myths are true in a scientific way as well. It's further undermined by the fact that the destruction of religion is the stated goal of the Templars, the people Altaïr is fighting. Then you remember that Altaïr is in control of the Apple of Knowledge and the thing has a One Ring-like effect on people's minds.
It helps to understand Altaïr may also believe that while All Myths Are True, the nature of the truth invalidates any religious truth from the stories. Likewise, he may just object to the methods of the Templars as opposed to their goals.
One of Altaïr's victims back in 1, Sibrand, also saw through the Piece of Eden and found oblivion in lieu of an afterlife.
You have to wonder why Ezio and his brother move like champion acrobats and Le Parkour masters even before they've had any assassin training. Then, duh, of course, you remember that they're children of an assassin. Simultaneously, it might be In the Blood as well as their father preparing them in subtle ways for their life ahead.
It's also likely that they learned from friends and through dicking around in Florence. Apparently, if we're to believe the heralds it's become quite popular with the young men to run and jump on top of the roofs in Florence.
It's also implied/mentioned that Federico had been learning at least some Assassin skills from his father, presumably preparing them for induction into the family business (Federico has to be doing SOMETHING all day, and in his Codex entry it's said he no longer works at the bank after a Noodle Incident). He then passed them on to Ezio and in what might be a way to help keep the heat off the Assassins in Florence other young men as well.
In one of the earlier cut-scenes, we see Ezio's dad fully accepting Ezio's trouble with the law / escapades with women. He says it's because it reminds him of himself, but maybe he WANTS him to crawl around the city and get used to fleeing from guards.
Desmond doesn't have to be a direct line of descent. As the child of Assassins, it's quite likely that their various families intermarry. Desmond's Ambiguously Brown features help this as well.
Even before the retcon in Brotherhood, Ezio's shrugging off Rodrigo's gut-stab is foreshadowed by Altaïr doing the same thing early in the first game. And also inflicted by the Big Bad, though you don't know it at the time. Coincidence or Call-Back?
The reason that no one seems to age over the past twenty years. Remember that we're experiencing things as Ezio remembers them. Most likely Ezio just always remembers them looking the same regardless of age. His sister always looks 15 because in his eyes, she's always been his little sister.
Genetic memory works more like a video recording than it does like episodic memory. If it were more like episodic memory, itd be too unreliable for Abstergo to fund so much research for it (and a descendant using the animus wouldnt be able to relive their ancestors conception or birth, or any memories lost if an ancestor acquired amnesia). Its simply a minor case of Gameplay and Story Segregation.