Hamlet's priorities

Hamlet has a few problems in his life. These include:

-His father's death

-His uncle marrying his mother

-His mother marrying so quickly

-Not being king

One would think that his sadness comes mainly from the death of his father. As humans, we tend to feel love towards our father, and if/when he dies, we feel sad. Understandably, he is upset that his uncle married his mother. Although he is upset, I believe that this doesn't seem to account for the majority of his depression. It seems that what upsets him the most is that his mother moved on so quickly. This is connected to his uncle marrying his mother; however, I would bet that should this wedding have occurred a few years after Hamlet senior's death, Ham. Jr. would not be nearly as furious. As a small side not, the fact that Hamlet is not king (which maybe he should be) doesn't seem to bother him; or if it does bother him, he at least does not express it to the reader.

As a side: I understand that if Hamlet's dad died and Hamlet senior's ghost is like walking around the Hamlet would like to talk to his ghost dad, but doesn't it seem like Hamlet is obsessing over it a bit much? The questions he asks are very strange and specific like about his facial hair.