Grammatically speaking, the last two examples are quite different. In the first example, what substitutes the predicative
The wisdom behind education is something.
What is the wisdom behind education? (question is about the predicative)
I don't know what the wisdom behind education is. <-- correct
I don't know what is the wisdom behind education.<-- too colloquial, unacceptable in formal writing.
Now, in the second example, what substitutes the subject.
Something is on her mind.
What is on her mind? (question is about the subject)
I don't know what is on her mind. <-- correct
I don't know what on her mind is<-- incorrect
