Is "Anh ấy nói trong khi anh ấy ngủ" also acceptable?
Yes but adding anh again is redundant.
Anh ấy nói đang ngủ was refused. Why?
Maybe because at this level, when đang was not yet introduced, it is always wrong?
This makes sense, thank you. The problem is the algorithm: theses exercices are coming anytime during the course and not all the acceptable answers are everywhere consistently registered.
In this situation, he say in his dream. While = trong khi.
I see your point, but still, it is a matter of context or interpretation: impossible here to know exactly what is all about.
Why not "Anh ấy nói trong khi anh ấy ngủ?"