Why पर not में?
में could also work.
The latter sounds better to me too.
My Hindi teacher told me both "men" and "par" mean location or place. Often "par" is used in same way where "at" is used in English, and "men" where "in" is used. Here it's exactly the case - "at home" is "par ghar".
Said no Indian parent ever.
Solution does not correspond to the above translation
Does पे work instead of पर?
Yes. They are interchangeable.
घर पर मत पढ़ो sounds strange - it literally means do not study ON the home. घर में मत पढ़ो should be the better answer.
My is right