The answer is hyperactive. The word hyperactive refers to extremely active or abnormally active. Hyperactive is the adjective form of hyperaction. Hyperactively is the adverb form. The work inactive refers to being not engaged or not working while the word reactive refers to the acting in response to a situation.
Henry's charactrization by the author in Red Badge of Courage is done through the thoughts Henry has. He is always referred to as "the Youth," and what he feels and thinks is narrated, unless he is engaged directly in a dialogue. He is the main character of the book and the novel tells his growth from an immature teenager to a war-weary adult.
You might read the Odyssey to get an closer insight on the culture or politics of the time. Also, you might wan't to learn more about Odysseus and his journey just for fun.