If I understand your example correctly, you're looking at the difference between subject and complement.
Who do you think that woman is?
Who do you think is that woman?
We should be able to turn these question back into statement form. We just go through the question-forming rules backwards.
We can move "who" from the front of the clause to whatever place it seems to make sense. Since it's an unanswered question and we don't really know what "who" represents, I'll just use a placeholder:
do you think that woman is [???]
do you think [???] is that woman?
Next, we can move the auxiliary in front of the verb that it governs:
you do think that woman is [???]
you do think that [???] is that woman
If we suspect that we don't need "do" in the statement, we can simply drop it:
You think that woman is [???].
You think that [???] is that woman.
To my native speaker's ear, it is more natural for the unknown -- the heart of the question -- to be the complement rather than the subject. If I'm answering in full sentences, I'm more likely to say, for example, "I think that that woman is the president" rather than "I think that the president is that woman".
The subordinate clause is copular. The subject of such a clause represents that which possesses a state.* The complement represents the state so possessed. Questions about either are logically and grammatically possible, but questions about the latter tend to make more sense.
* I still don't have a good label for this semantic role. I opened a question on ELU, but the good people there can't seem to tell the difference between that which possess a state and that which undergoes action without change. Until I get a better answer to that question, I can't offer a better answer to this one.