Um, I agree with the other posters here to a point, but wanted to empathise with you and your DH regarding the constant questions. It can be very tiring to answer endless questions and to maintain a constant dialogue with a small child, especially if, by nature, you have a short fuse and are quite introverted and quiet. I appreciate it can get to the point where you need some quiet time without the constant stream of consciousness interrupting your own thought patterns.
I think it's worth sitting down with your DH and working out a way of dealing with the constant questions in a way you're both happy with. Your DD is old enough now to understand limits and she may need to included in a conversation once you and your DH have decided how you're going to approach this.
It may be worth agreeing a consequence for 'cheeky' responses from your DH - the rest of the day in her room probably is just making her madder and madder at your DH, so it might be worth coming up with a consistent and predictable consequence that is proportionate. It might even be worth having a special, secret word that DH can use to your DD to indicate that he's getting to the end of his tether with conversations and questions?
I do empathise - I have a DS7 who chats and questions non-stop, and I'm a quiet person by nature, so find myself having to constantly check my own irritation in order to deal with him in a constructive way. There are some days (work stress, and other issues) where I just can't deal with it, so I find a way for DS to amuse himself for a while so I can get my head together -- or I find an activity for us both to do that is stress free for me. Personally, I find that reading to him is very relaxing, but so is a game of cricket or a game of top trumps. I'm also partial to playing dress ups with Action Man. Maybe you and your DH can think of a few strategies to give him the space to manage his own emotions - and think of a few non-stress activities they could do together?