If you say, "What are you", it means, what makes you up? So if you were talking about your citizenship, you could say, "I am French, what are you?" "What do you," is not a proper sentence. You could say, "What do you do?" which would mean that you were most likely asking what sort of job someone works at. "What are you think," is also not a proper sentence. However, "What do you think," is a very common sentence and is asked when you want someone's opinion about something.

I recommend that you specifically study and practise using the verb forms of the present simple - affirmations, negations, and questions. The verb forms are fixed. The rules on this do not vary.