Someone says, "What makes you think that way (like that)?" or " How did you come to that conclusion?"
My question 1: Do you say "How do you think?" in this situation?
No, we do not say "How do you think?" in that situation. In that situation, we say:
- What makes you say that?
- Why do you say that?
- What brought you to that conclusion?
My question 2: Is "How do you think?" acceptable in a particular situation in daily conversation, except when you want to know the mechanism of human's thinking process?
The question "How do you think?" is fairly common in informal conversation, but it is not a nice thing to say. It is a sarcastic rhetorical question. The meaning is not commonly the literal one that you give above, which is also possible.
"How do you think?" (also with other wh-words) is generally used after someone has just asked something to which the answer is obvious. The meaning is that the asker should already know the answer to his or her question. For example:
A: How did you open the door?
B: How do you think? I used the key.
A: Why are you writing a thousand-dollar check?
B: Why do you think? It's the first of the month. Rent is due.
A: Where are the fish ordinarily?
B: Where do you think? They were taken out of the ocean.
A: When do we leave?
B: When do you think? You have your plane ticket in your lap.