I agree with Serelonde, especially about how to fix E.
Also, I don't think your student's sentence is wrong, just... awkward. Certainly unnatural but I can't think of a reason it would be ungrammatical.
I wouldn't use the hyphen in C (or any of them).
Also, while the sentences (except E) are correct they feel like textbook examples. We would almost never say 'The school is a ten minute walk away.'
We might say,
School is a ten minute walk away. (usually understood to mean 'my school', or 'my child's school', depending on context; possibly an arbitrary subject's school in a longer context.)
My school is a ten minute walk away.
The high school is a ten minute walk away.
There are probably contexts where we would say 'the school'... perhaps if it were the only school in town for example. Also possibly if the school rather than the walker is the topic of the conversation.
You might also say,
My school is a ten minute walk from here.
My school is a ten minute walk from home.
These are less ambiguous and pretty natural. For some reason I feel like b/c/d don't need that disambiguation, the natural assumption in most contexts will be that it is the walk from home to school.