A. How did you get here?Do you think by saying "How do you think?" B is expressing the same idea as "Why do you ask?"
B. By car. How do you think?
A. I thought maybe you walked.
A. Why do you always get good grades?
B. I study. How do you think?
No, or at least not directly, Teleostomi. In your first group of sentences the question means " How do you think I got here ? " This answer usually suggests that the person thinks the question was unnecessary and/or that the answer to the question is obvious.
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Inchoateknowledge"How, do you think" is informalNot at all. "How" means by which method or form (of transport), for example). "What" means what is your view/opinion, there.
It is like "How? -- do you think."
"What do you think" is better here.