1. Do you think why he is upset?
2. Do you believe where he lives?
3. Do you suppose where he was born?
(Do you have the reason why the three sentences are not correct? Do you have any logical reason?)
4. Why Do you think he is upset?
5. Where do you believe he lives?
6. Where you suppose he was born?
(These questions are right, aren't they?)
The main verb used in each of sentences 1, 2, and 3 doesn't make sense. Here are some possibilities:
Do you know ...
Do you wonder ...
Why is he upset, do you think?
Where do you believe he lives?
Where do you think he was born?
4-6 are all correct, yes.