Thank you very much for your corrections!

Here are some more sentences I need you to revise.

1)There is the appearance of a ghost which urges the hero to commit the revenge. (Correction: to avenge, get/have/take revenge on Claudius/to seek revenge for his own murder).
2)A violent crime made to the hero’s family. (Correction: A violent crime has been committed/was committed against a member of the hero’s family.)
3)Hamlet has a period of doubts in which he carries out his plan of revenge (is “vengeance”) possible?
The hero has a close relationship with the audience through the asides. There is a lot of bloody action and a lot of deaths occur throughout the play. (There are many bloody actions is possible??)
4)The ghost of the previous king, Hamlet’s father, appears to Hamlet.
5)The most particular thing (correction: the main feature?) of the play-within-the-play is that it is formed from two audiences: one is the real audience, the other is the one on stage.

1) A ghost appears and urges the hero to avenge the dead man's death.

2) A violent crime was committed against a member of the hero’s family.

3)Hamlet has a series of doubts as he tries to carry out his plan of vengeance.

The hero has a close relationship with the audience through the asides. There are many scenes of bloody action and several deaths throughout the play. (Using "a lot of" leads to awkward sentences and sometimes problems in subject/verb agreement. Avoid the phrasing.)

4)The ghost of the previous king, the elder Hamlet, appears to his son, Prince Hamlet.

5) The main feature of the play-within-the-play is that it includes two audiences: the real audience and the one on stage.