Hello I agree with Guillaume. If Bayldon is asking a question with "studied casualness" then it means that he is working very hard at trying to appear casual (like he's not making any effort at all), and so he isn't succeeding because it is obvious to the people around him that he is not acting naturally at all. It's impossible for a person to act as if they are naturally "calm and casual" if it takes an effort to do so. I hope that helps!

This phrase is suggesting that Byldon has thought about how he can appear to look casual. He is trying to look relaxed, not worried, and friendly. He may not really feel the way he is acting.

Hello ! "Studied casualness" is what we call an oxymoron, that is to say, a self contradictory expression. To be casual is supposed to mean to act naturally, unprepared. If Bayldon's "casualness" is studied, it means that he has thought about it in advance, that he has worked on it : he is not really being casual. He wants to appear to be casual, but is actually self-conscious.