- "Which (one) do you think he is?"
- "Which (one) do you think is he?"
If they are both grammatically correct, what is the difference in meaning?
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Think about the difference between "I think that one kissed him" and "I think he kissed that one".
As a question, "Which one do you think kissed him?" is used where we are asking about him as the object of the action, whereas "Which one do you think he kissed?" is used where we are asking about him as the subject of the action.
Now think about the difference between "I think that one is him" and "I think he is that one". Unlike the kissing examples, they mean essentially the same thing, with just a difference of emphasis.
One of them becomes "Which one do you think is him?" and the other one becomes "Which one do you think he is?".
In very formal English, the verb "be" takes a nominative complement (as in "It is I" or "That is he"). So the first of those two questions could also be worded as "Which one do you think is he?" (very formal).
All three are correct. Generally the first one is the most usual wording.
Finally, because (without the "do you think" clause) the usual wording is "Which one is he?", you could also word it as "Which one, do you think, is he?". By offsetting "do you think" and making it parenthetical, that wording loses its slight oddness and becomes no more formal the other options (although still a less likely choice of wording).
Similarly, "Which (one) do you suppose is Alexander Grayson?" and "Which (one) do you suppose Alexander Grayson is?" mean exactly the same thing. There is just a slight difference of emphasis. The first one corresponds to the discovery that "That one is Alexander Grayson!" or "That's Alexander Grayson!", while the second one corresponds to the discovery that "Alexander Grayson is that one!".
Here, the first wording ("Which (one) do you suppose is Alexander Grayson?") is most typical.