Why is there a di on here? Usually one can just write 'I' in front of family members
I wrote 我的姨 is that wrong
I don't think 姨 can be used alone like that. The word is 阿姨. The 的 is optional for family relationships, but it's better to leave it out.
Doesn't 很 mean "very"? Wouldn't that change the meaning of the sentence to "My aunt is very smart."
Technically, 很 means "very", but that meaning is often de-emphasized. So, 她很聪明 can be understood as just "she is smart". If you want to emphasize how smart she is, you could say something like 她非常聪明. (非常 = "extremely")
Since 聪明 is already a two syllable adjective, shouldn't it be okay to leave out 很？
An adjective can't stand alone as a predicate (except in certain direct comparisons). That is the reason for using 很.
Could I say 她当老师 as well here?
In the very lesson where we are supposed to learn that the 的 is optional for family members, its omission is marked wrong. Incredible.