Re: teenage immature Cleopatra - partly because of a misunderstanding on Shaw's part of Mommsen's Caesar (one of his key sources), which lists Cleopatra's age when the Egyptian civil war started, but by the time Caesar show's up, several years have passed - but partly because of the parody intent. Cleopatra for the late Victorians was the sinful woman (never mind that the only men we know for sure she had sex with she considered herself married to), threatening empires, and to present her as a childish teen whose relationship with Caesar is completely platonic was a deliberate reverse of expectations. (As you say, it's not just a question of her age, but a deliberate authorial choice - Shaw's Joan is also a teenager (as she was in rl) who does some growing up through the two years covered by the show, but she's never childish.) With early Shaw, it's always worth checking out the theatre habits of his day because as many a socially engaged author, he does a lot of parodying. (The very first play, Arms and the Men, parodies the type of Ruritanian swashbuckling adventure in fashion then.) Most obviously with Britannus as the parody of the audience of Shaw's day, but also Cleopatra as the reverse of a femme fatale of the fin de siècle.