“To allay” (allay) means to make someone stop worrying about something, or to make something stop being a problem.
Shawn could have asked whether Hannah had answered Chris's question, and that would mean the same thing as allay.When we say that you “allay” someone's concern, we mean that the person has an answer to their question, and they are no longer worried about it.
You can answer someone's question, however, without allaying their concern; they could understand your answer but still be worried about it.So, Shawn is asking whether Chris has had his concerns allayed by Hannah.
Chris nods (nods) his head, or moves his head up and down to indicate that yes, his question has been answered.We use this verb “to nod” when we are talking about saying “yes” by moving your head up and down.
If you're going to say “no,” moving your head from side to side, we would probably use the verb “shake” (shake).So he shakes his head “no,” but he nods his head “yes.”
Chris is nodding his head, saying that his question has been answered and his concern has been allayed.