Finally watched the first ep. It was good. But the whole part about Joker in that math class made no sense. He…
That teacher was basically one of the five teachers involved in making the question paper. As upstairs quoted, it was indeed done illegally as he was basically giving out possible questions in his test. His parent did ask if he is utilising the tutor properly and he did reply he's studying the material given by the tutor. So it was simply a test at the tutor's. The main examination wasn't shown. He didn't recognise it was Joke because it was written "Joker" not Joke and he did place the paper on the other guy's place. Also I don't think they are that friendly introducing themselves to other students. (He may have put on the disguise and went ahead as another in order to avoid disclosing his real identity which doesn't make much sense.) And yeah, I don't know about the rest you're asking about.
This might be bad subtitles or translation but the son of the empress dowager is Prince Xian but there's a female…
I understand what you're taking about. Princess Yong'an has another title as Prince Ying (Wang may be Prince/King) but it's merely a title in her case. She's not like a 'king' king. I hope you understand. In Chinese dramas, usually the Prince/Kings are the subordinate's of the Emperor who's the supreme power there. Usually the Empress Dowager is the previous Empress of the dynasty, who in this case is the current Emperor's (the kid) paternal grandma. Princess Yong'an and Prince Xian are the children of the ED, aunt/uncle with respect to the current emperor. The previous Emperor was the ED's son.