All these are correct.
तुम खाते हो। Tum khaate ho.
तू खाता है। Tu khaata hai.
आप खाते हैं। Aap khaate hain.
I suggest using the last one for formal situations or with the people elder to you and the first one for informal situation or when you are talking to younger people. Avoid the second one as its considered very rude in many states across India.
What makes the second one rude? Could you please translate each one? I am guessing that there are three different ways of saying "you". (I know languages with 2 different ways of saying "you" (formal and informal), but I am confused by the fact that you have listed 3 ways.)
I would like to say something that if you want to say something to your elders say "आप" because it is formal and shows well mannered and kind of someone. Use "तुम" to say it to your friends or your younger ones. It is also formal And "तु" can be used to your friends. It is informal and don't use it in front of your parents or elders otherwise there would be a huge problem.