1) The cup:
The cup represents the King's union with his land which leads him to damnation, this was also an issue for the late King Hamlet but he didn't know it. In this case King Claudius knows that the only way to spare his soul is to give up the land but instead he chooses damnation.
In the first scene when Horatio and Hamlet walk up on some gravediggers Hamlet asks about a skull that one of the gravediggers had pulled from the ground. The skull belonged to Yorick, the late King Hamlet's jester who Hamlet had a personal connection too. After seeing the skull Hamlet begins to ponder life after death and how even the greatest men throughout time such as Alexander the great become no more than dirt. The skull represents death and therefore Hamlet's confrontation with death.
3)Sir James Hales:
In act V scene I Shakespeare alludes to Sir James Hale a Justice of the Common Pleas.