to buckle down means to apply yourself diligently to your work, or a task. It is time for you to buckle down and study hard if you want to pass your exams. to not give a hoot, means you couldn't care less about something - I don't give a hoot what she thinks of me! to stand a chance, means to have a chance of something. You don't stand a chance of passing your exams if you never do any study.

Some examples: Last semester I didn't study hard and I failed. This year though, I'm going to buckle down! (start working or doing sth seriously) I don't give a hoot if they accept it or not. (I don't care) You still stand a chance to pass the test. (there's a prospect of success)