The ghost might repressent the feeling of shame and betray that the old King Hamlet, h and his son feels. The queen can not see the ghost because she doesnt feel guilt, she doesnt think it was wrong to marry the kings brother 2 months after his death, and because everyone else can see the ghost they understand what is wrong with her actions where as she doesnt.
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The ghost warns hamlet not to do anything to his mother, but to "leave her to heaven".
You cannot see the ghost hamlet
He speaks to the ghost of his father, which she cannot see.
The Ghost tells this to Hamlet in the play. It means that Hamlet should not harm Gertrude but rather let Heaven (and subsequently God) decide her fate.
The ghost tells Hamlet the secret of his father's death. Hamlet's father was not killed by a serpent, but was murdered with poison. He also told hamlet that it was his uncle who murdered his father, and that he also seduced Gertrude, his mother. The ghost then tells Hamlet to avenge his father's death but to leave his mother alone.