It seems to me that the questions most likely to be asked in any examination on Shakespeare's Hamlet would include these:
Is Hamlet really mad?
If not, why does he pretend to be mad?
Why is Hamlet so indecisive?
Why doesn't Hamlet kill Claudius with his sword when he comes upon Claudius at his prayers? (This question is of the greatest importance because it involves the main theme of the whole play, the so-called "Hamlet Problem." Why doesn't Hamlet act as he is supposed to act, as he is obliged to act, as he has sworn to act, as he keeps urging himself to act?)
I realize that these are not exactly themes, but they are closely related to themes. The questions have been asked and answered many times in eNotes, and you can get some good ideas by referring to them under the Q&A section under the topic heading of "Hamlet by William Shakespeare."