Kessler is basically Cole from the future. He came back to the past due to the “beast” threatening his world, so he came back in time to shape up Cole and ready him for the future.
Sasha is the leader of the Reapers. Before the explosion she worked with the First Sons and also had a “relationship” with Kessler.
What/Who is “beast”?
From what I know the beast is a superman just like Cole. I think that he's the main antagonist of inFamous 2 and hes the reason why Kessler came back in time.
Who is Alden? Alden used to be the leader of the First Sons until Kessler game and took over. After that he wanted revenge and so became the leader of the dust men.
What are dead drops?
Dead drops are voice recordings left by John White (i think that was his name either that or Jack White). The recordings talk about things such as things like the relationship between Sasha and Kessler.