Translation:Their teacher has very high standards.
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".
Um, you need to restructure your sentence.
Originally your 要求 is a verb. 很 can't modify an verb unless it is a modal one like 能, 愿意, 应该, 要(not very often) and such.
It's standard. Consider "ta hen neng chi" or "wo hen xiang zou".
Negated you must add "shi": " ta bu shi hen neng chi" or "wo bu shi hen xiang zou".
That would require a 有 to show that the teacher has the standards: 他们的老师有很高(的)要求. Without it, the standards are the subject of the sentence, not the teacher. :)
What about, "Their teacher's requirements are high"? I always assumed it meant both standards/requirements.
Total failure of colloquial English in the translations in this course.
Is it also correct to say 他们的老师的要求很高 ? Or are too many uses of 的 to be avoided?