1. The sentence is unfinished. It probably finishes with 'voice' , 'tone of voice', or similar. We say things IN a particular voice. The preposition 'in' is connected to the basic noun phrase "a jaunty tone of voice" and the extended noun phrase "what he thought was a jaunty tone of voice". It means that George was trying (unsuccessfully) to greet his mother in a cheerful and carefree way. 2. This is not an idiom. It means exactly what it says. There was a withered hand on a cushion which was displayed inside a glass case. A glass case is a box with glass sides and a glass top, used for exhibiting objects in museums. 3. This is a rhetorical question. The speaker is unhappy that he is not on the House team. The word "that" refers back to a statement in the previous sentence. I presume the speaker's friend has just tried to cheer him up by saying something positive. But the speaker responds by saying that this doesn't help. He says that "that" - the positive situation which the friend has just mentioned - is of no use to him if he isn't on the team. NB These explanations would have been a whole lot easier to do if you'd only given more context!

1: You have left something out after jaunty. You should write it as was a jaunty... with the ... meaning 'I've left the rest off'. The 'what' serves to link the two logical parts of the sentence: "Morning mum", said George. George clearly thought he said that in a jaunty (way). You could say "Morning mum", said George, in a jaunty (way). But the important difference was not that it was 'a jaunty way', but that he thought it was jaunty when he said it. 2: A 'glass case' is a case made out of glass. It has glass sides so you can see what's inside it. No, it's not idiom. There was a hand inside the case. The hand was withered (dried out). The hand was sitting on a cushion. 3: You could read it as 'what benefit is (that) if I'm...' 'that' is whatever they were talking about previously. It must be related to being on the team.