If I get pulled over for DUI do I have to answer the officer’s questions?

The short answer is no. The fifth amendment to the U.S. Constitution provides that no person shall be compelled to be a witness against themselves in any criminal case. DUI is a criminal case so any answers that you give the officer can be used against you. Therefore you have the right to refuse to be a witness against yourself. The officer may be asking questions about where you are coming from or how much have you had to drink. The answers to those can be incriminating so you are not required to answer those questions.