Generally, when you form a question in English, you perform three processes:
- If the main verb is neither an auxiliary verb nor a form of "to be", then replace the main verb with a conjugated form of "do" followed by a bare infinitive.
- Put the main verb before the subject.
- Pull the question word to the beginning of the question.
However, process 2 is generally only done in direct questions—questions that you are asking someone as a complete sentence which stands alone. In indirect questions—questions are used as pieces of another sentence—process 2 is not performed.
The question "How old do you think I am?" is a direct question where processes 2 and 3 are applied. So first we have the question word (which is actually two words, "how old"), then the main verb, then the subject.
The question "Do you know how old I am?" is a yes-or-no question which contains an indirect question as a subordinate clause. That indirect question is "how old I am". Since it's an indirect question, process 2 is not applied. And since the entire question "Do you know how old I am?" is a yes-or-no question, it has no question word and process 3 is not applied.
"Do you think how old I am?" sounds like nonsense. The question word is "how old", and it should have been put at the beginning of the question in order for the question to make sense.