I may be wrong but I believe 'is he' is rejected because 'mlada' is feminine, implying you are asking about a female when followed me a non-gender-descriptive term like "je" for he/she. If it was "mlady" then he would be the correct term.

Because the Czech version too emphasizes the word "young" and isn't the general way to ask for one's age.

In English these are not the same question either. Maybe how old is she compared to what is her age are the same but how young is she has more to do with the subjectiveness of the answer.