1. Hamlet's tragic flaw is everything enlisted above, except for 'a melancholy love sickness which leads to temporary insanity'. He wasn't in love, not really, so this sentence refers to Ophelia, not Hamlet.
2. Hamlet pretends to be insane so as to 'conceal his attempts to get information regarding Claudius' guilt'. He didn't want his uncle to realize what he was trying to accomplish, so it was easier for him to pretend to be mad so that nobody would pay any attention to him.
Answer:
A. All I can say about my rival's idea is that he's a thief and he should
be ignored.
The protagonist would be the main (or one of the main) characters in a narrative, while an antagonist would be the villain. The antagonist does not have to be human. An antagonist can be sickness, natural disasters, an animal, or anything else that gets in the way of the protagonist.
So the answer would be C. An antagonist.