Turandot/Headscratchers

Okay, so the basic plot is that before the suitor comes, Turnadot had been executing various other suitors/princes because they have failed to answer her riddles three. In the beginning, we see her having a Persian prince beheaded. Here is what troubles me: Why isn't Persia getting all up in arms about her lopping off one of their son's heads? I know it's just a play/opera, and I need to relax, but it's just a bit of Fridge Logic when you think about it.

Not to sound sexist or anything, but the supposed "Grand Emperor" really has let his daughter walk all over him. If he didn't like her idea of 'killing off suitors', why didn't he tell her something like, "You will marry this man! I do not care if you like him or not, you will marry him and you will give me an heir!" Again, I don't mean to sound sexist, it's just that...his behavior is kind of odd for a grand emperor...