Paul wants to be able to deal with Mitchell, as his sister is able to. Paul says " But Cassie was not only beautiful, she was tough, smart, and just a bit cocky," meaning that she is more than just a pretty face. Paul also says he has a problem with Mitchell ("At first I just tried to stay out of Mitchell's way, but that didn't solve the problem.") Paul is trying to deal with that problem, and that is why he talks to his sister.
Invention, is the method used for the discovery of arguments in Western rhetoric and comes from the Latin word, meaning "discovery". Inventio is the central, indispensable canon of rhetoric, and traditionally means a systematic search for arguments.
In September 1642, just after the First English Civil War had begun, the Long Parliament ordered the closure of all London theatres. The order cited the current "times of humiliation" and their incompatibility with "public stage-plays", representative of "lascivious Mirth and Levity".