The first game is not set in 2003 as we know it.Numerous reviewers commented on the retro-futuristic atmosphere of the first game: the setting is reminiscent of Escape from New York, while the music owes a great deal to it and other films by John Carpenter. And of course, the very premise presupposes some kind of violent, lawless society. Yet incidental dialogue in the last mission makes it abundantly clear that the game is meant to be set in 2003. Perhaps the game is actually set in an Alternate History or something to that effect.
Daniel would regain his memories when he gets to his new place.Well, I wouldn't want him to lose his memories forever. One thing for sure is that when he sees his two kids again in the new place, he'll get his memories.
James Earl Cash, Daniel Lamb, and Leo Kasper are all Assassins.All of them are innately good at stealth and murdering unsuspecting targets, and all fight against conspiracies involving the government (albeit none as grand as the one Desmond and his ancestors fight). Hell, the Pickman Project, which gave Daniel his Leo split-personality, was strictly meant for the training of "Assassins"!