I have answered parts 1 and 2, but I am not confident enough to answer parts 3 and 4, sorry.
1a.) A Greek drama is a is a play which was performed in ancient Greece, most notably the tragedies.
1b.) The actors in Greek theater were called hypocrites, I believe. The Greek spelling the was "hypokrites"
1c.) The Greek word "hypokrite" is a compound word which translates to "an interpreter from underneath." This is because they performed while their faces were hidden underneath giant masks so the ancient audiences could easily tell characters apart. More information can be found here: https://www.merriam-webster.com/words-at-play/hypocrite-meaning-origin
1d.) aside from the actors there was a chorus, which explained necessary information to the audience, usually in song form. Eventually this evolved to be a more active role in the plays.
1e.) The plays were performed in open air theaters (theatron), the most famous of which is at the acropolis in Athens. They were shaped like a bowl for acoustics.
2a.) Pericles descibes Athens as a place of beauty with time for relaxation, "When our work is done, we are in a position to enjoy all kinds of recreation for our spirits."
2b.) Thucydides describes Athens as a place which forces men into "continuous labor."
2c.) In Pericles opinion, Athens is a democracy because the power is in the hands of "the whole people," meaning it is not ruled by a king or small group, but rather by the public.
2d.) I do not think Thucydides would consider Athens' role in the Delian League as democratic because Athens kept the league together despite protests of those who wanted to leave. He also says, "at first" the rulers of Athens were different from the old rulers, implying they were no longer different from them at the time of the quote.