I left out three sentences. Could you please check them too? I did some of the corrections myself.
1) Hamlet has been troubled since his father _________ in tragic circumstances.
(died, was murdered but not "has been murdered"?)
His uncle Claudius _______ to the throne (succeeded to the throne: is it the only choice?)
2) Laertes's poisoned sword kills _______, the________ and ______himself.
(Hamlet, King and Laertes himself/he himself is a mistake?)
3) The ghost of Hamlet’s father appears in front of Hamlet and Horatio because he wants to explain how he was killed and who killed him. The play ends with the deaths of Laertes , the King, Queen Gertrude and Hamlet who told Horatio that Fortinbras should be elected King.
4)Correction: the ghost of the old King appears to Hamlet and Horatio because he wants to explain to them how he was killed and who killed him. The play ends with ….. who tells Horatio that Fortinbras should be elected king.
1. "was murdered" -- yes
I'd say "in suspicious circumstances"
I'd also say "Claudius took the throne..."
2. Laertes's poisoned sword kills Hamlet, the king, and himself.
(You cannot use "he" here because these words are direct objects, not subjects.)
4. The ghost of the dead King appears to Hamlet and Horatio because he wants to explain to them how he was killed and by whom. The play ends with the death of Hamlet, who tells Horatio that Fortinbras should be chosen king.
(Believe me! In the 1200s, they did not hold elections as we understand them!!)