Connor's relationship with Haytham is complicated. Here, where he has no war to fight with the man, he has to come to terms with the fact that he doesn't know what he wants from his father, and has to deal with the reality that asking anything of him is going to put a strain on his relationships with every other assassin in Haven.
Just before coming to Haven, Connor had to deal with the fact that the most important person in the world to him had fallen ill and, at his age, was unlikely to recover. After he spent several weeks in the city Achilles appeared... only he is several years younger and Connor has been spending a significant amount of time getting on his mentor's nerves by being generally overbearing and worried at him. Also there's the fact that he won't kill Haytham even though he's got all the opportunity in the world and nothing to stop him right now...
Kanen'tó:kon was Connor's closest childhood friend, before Connor killed him over a misunderstanding that put them on opposite sides of a war. Now that he's in Haven, Connor is torn between being beyond happy that he's here and alive and they get a second chance, and being crushed by the guilt of what he did to Kanen in the first place and not knowing how to tell him. 8C
Despite the weirdness of Desmond's claim that he's one of Connor's descendants, Connor pretty much believes him. Also he answers all of Connor's super dumb awkward questions and only laughs a little.