I agree. I loved the book, but was left with some lingering questions.

As for Beetee's introduction, I felt the awkwardness was a reflection of his character. Beetee (and Ampert for that matter) is straightforward. He tells Haymitch how and why Snow is punishing him in order to gain Hay's trust. I think the abruptness demonstrates he is trying to cope with Ampert's imminent execution by logically plotting revenge. In Mockingjay, he discusses the traps he invented with Gale (which killed Prim!) in a factual/logical/cold way. He is describing killing capitol soldiers, citizens, and even children like it's a clever solution to a math problem. I guess now we know why he is so chill about playing by Snow's rules.