Possibly, they just might! Depends on how things go between the two of them.

And Chara's dislike of knights stems from knowing Undyne, since if you know of both her fights (Pacifist and Genocide) she's a complete pain in the ass to fight. So the hate towards being beat by her a few times has led to just a general dislike of all knightly types.

As for Chara trusting people? Who knows, it'll take a lot for them to trust anyone human that's for sure.