It can. The problem is with their English translation. 要求 means what the teacher is asking for, or what the teacher is demanding. So the English would be better off as "Their teacher demands a lot", or "Their teacher asks for a lot". Your sentence is fine as well.
No, I don't think it can be. That would translate as "他们的老师是很要求多的。"
The important part of the sentence is "很高“, which means "very high" rather than just "very".
You might also hear someone saying "你的中文水平很高“, which means "Your Chinese level is very high".
Leaving the "very" out was incorrectly marked incorrect. Often 很 modifying a stative verb/adjective (such as 高) isn't translated as very, even though it's a required element in the absence of another modifier.