Why is the idea of playing a role or acting a part so important to hamlet over the course of the play? how does role-playing affect several major events in the plot and the relationships between various characters?

Hamlet was role playing throughout the whole play and acted crazy all the time so that he could revenge for his father's death.

Hamlet thinks that when ultimately he kills the King Claudius, nobody else will kill him as everyone believed that it was the result of the case of insanity that was brought in notice by his father's death.

Moreover, he waited for a little time to plan and postpone his promises that he had made with the ghosts and tries to hide his true feelings because he didn't want anyone to know about his real feelings i.e. to plan his uncle's death.

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i think the answer is invented words, rhyming knack, alliteration, and, metaphor.