I don't like either number one or number two. Two would be okay if it was "...what did he become AT his school" or "...what was he chosen for AT his school" would be better yet.
Number one could mean anything. He became? One does not just become captain or any other social or elective position (or become appointed to a position). One may become some personal attribute, like learning to read and write, thus becoming literate, or, by long study someone might become a doctor. He might have become captain when the principal chose him for that role, or after he was elected to it. To become something implies a cause of some kind. It doesn't happen by itself. Number one is too vague.
1. In grade seven, what did he become?
2. In grade seven, what did he become of his school?
3. He became the captain of his school.
[#3 is the answer either #1 or #2. Are both answers correct? Which one is the better of the two?]
2 answers
I'm not sure I'm clear about "of" and "at". He would become captain of or at his school. Number two just doesn't make sense to say he became OF his school.