In general, entering the USA is a right of U.S. Citizens and Permanent Residents. But they can detain you without a warrant if they don't like your answers, and they can arrest you if there are outstanding warrants on your record or if they find you in violation of customs or other laws.

Overall, most immigration questioning is routine--they care less about the answers then about HOW you answer. If you seem anxious, or have trouble coming up with specifics, they might get suspicious. I almost never get any substantial questions at all. Usually, just "Where were you traveling? How long were you there? What is your occupation?"

Once, when I was connecting through YYZ, I was sweating because I had run from my arriving flight and was late for the US-bound connection. When I got to the immigration inspector at preclearance, the guy asked me a more substantial battery of questions, most likely because I was prespiring and he wanted to see if he could trip me up.