You can say just 'yes' or 'no', but if you don't say anything else after it, then the answer can sound incomplete. You might say: 'Does she like pizza?' 'No. She's allergic to wheat and cheese, so she doesn't eat anything like that.' but 'Does she like pizza?' 'No' can sound a bit abrupt, and may even seem a little rude. That's why we use the 'echo' response to complete and confirm the answer. By the way, please note that 'do' is ONLY used for the present simple and past simple tenses. In all other forms, you repeat either the modal verb or the appropriate auxiliary verb. Will she eat pizza? No, she won't. Can she eat pizza? No, she can't. Was she eating pizza? Yes, she was. Has she eaten pizza? Yes, she has. Is she going to eat pizza? Yes, she is. Had she eaten pizza? No, she hadn't. Please don't make the mistake of thinking that 'do' is an all-purpose response.

You can reply to yes or no but I sincerely encourage you to use more long sentences. The Do/Do not are used to not repeat the whole sentence Are she eating a pizza? Yes, she is eating a pizza/Yes, she does...