To be honest, I don't like either of the sentences. "Mom asked me questions about my teacher" is much more natural.
I'm a teacher teaching English in Korea.
One of my colleges said,
the sentence "Mom asked questions about my teacher of me." is grammatically correct,
but the sentence "Mom asked quetions of me about my teacher." is not.
As I know of,
When there is not a modifier, "about my teacher", which modifies the objective case questions
the former is correct. ( Mom asked questions of me.)
However, when there is a modifier, "about my teacher", which modifies the objective case questions,
the former and the latter are both correct.
As a rule, when writing English sentences, if there is a subjective case or an objective case which has a long noun modifier,
the modifier can be moved to the end of the sentence to make a subjective case or an objective case short; for native speakers of English
prefer to have a short subjective or objective case in sentences.
If I had to attribute grammaticality to those two sentences, I'd say they were both good. But they are not natural sentences, so it's not worth arguing the point - unless you want to tell us why your colleague thinks that sentence two is ungrammatical.