Is it all a coincidence?

In Act I the ghost of Old Hamlet appears only to tell his son the cause of his death. The whole thing is very mysterious because you can tell that the ghost is angry. His appearance in the scene is weird, and made me think why is there a ghost showing up. I immediately thought the situation wasn't going to be good. The ghost tells Hamlet about how he died, and who killed him. Hamlet believes him, but before acting on what his father tells him he thinks about whether or not it was really the ghost of his father. I think that Hamlet was smart with the way he tested out whether the information was true or not. By having the players act out the scene, they made Cladius react in a way that gave him away. Was there a reason for old Hamlet to show up two months after his death to tell his son of his murder? Was there any significance to the particular time that he showed up? or the place where he showed up? Why didn't he just go straight to Hamlet?
It's really sad because Queen Gertrude may have really been in love with Claudius. I personally believe that she is stupid to have even married her dead husbands brother. I think she should have known that the situation didn't feel right. Her son is acting weird towards everyone because his father died, but also because he knows the situation isn't right. His uncle is now the king, and sleeping with his mom. He knows that was not a coincidence and that the situation was really weird. So he showed his displeasure. How did Claudius get Gertrude to marry him? I can understand if it was a different person, someone that wasn't related to her son and dead husband. Did Gertrude not think that 2 months was a little to fast? Was that just a coincidence? Claudius had the situation planned out. He knew that anyone who married Gertrude would become king, and that Hamlet was the next in line.


To respond to this post, please try to give me some insight into what you believe are the answers I asked? Or your take on the situation.