Does Negan like Carl?
Based on Negan's interactions with Carl, I would say that Negan likes Carl's spirit, and he sees it as a way it could benefit him, and therefore if given the opportunity will do everything he can to manipulate it to his advantage.
Carl's obviously has got the nerves of a Grizzly Bear, and if you know anything about Grizzly Bears, there is very little that intimidates them. And if it wasn't for Carl's age, Negan would've killed him a long time ago.
Negan wants Carl to be one of his henchmen, and since Daryl couldn't be broken, it makes sense Negan might set his sights on Carl, given that he is young, and still inexperienced; even though he has been through quite a lot already.
Hell, if Negan had his way, he may even plan for Carl to replace Dwight eventually as his right-hand man. Negan would discard Dwight in a heartbeat if he found someone more vicious and more malleable.
So what do you think, does Negan actually like Carl, and do you think maybe if you might have any plans for him?