(Warning: Spoilers for The Fall) That old guy in the white suit wasn't the Mentor.
If you want to bring someone to meet you, the only rational reason to kidnap them instead of, you know, sending an invitation is because you don't trust them. And if you don't trust someone, why on earth would you leave them alone in a room with the head of your entire organisation and a deadly weapon?The Assassins aren't that stupid. They set up a convincing-looking stand-in for the Mentor in order to draw out possible traitors. The REAL Mentor is alive and well.
- The Mentor seems to want to hold certain mystique about his existence - hence the kidnapping. But according to his words, the Mentor isn't so much an individual than a collection of memories and thoughts of dozens or hundreds of people throughout ages. They can't have gone so long time with just one guy passing a torch to another - they must have the means to create a new Mentor, perhaps out of anyone with a genetic link to the original Assassin heritage. But the reason why the Assassins are in so great dissarray in the games is that Daniel told the Templars about all their major compounds, so it can't have been entirely planned out affair.
The Assassins are trying to train Desmond to be the next Grandmaster of their order.
After The Fall, the Mentor's dead, and the Assassins need a new leader. If they already have one, they're probably just an acting leader, ala Machiavelli after Mario was killed. After all, both of Desmond's ancestors played as so far were Grandmasters in their perspective generations, and Desmond even commanded a few Assassins through Ezio in Brotherhood.Daniel Cross will be a rival and maybe even antagonist to Desmond.
He's got a lot of Assassin skills, and he's defected to the Templars. In Brotherhood multiplayer, Abstergo was trying to use the bleeding effect to beat Desmond, after all...