No, you don’t understand. Sherlock knew John had written “Sherlock Holmes” since he answered “sometimes” to the first question.
When he asks if he’s tall he only does it to see what John would say and his answer only confirms his theory. And then he goes on asking if he is nice and clever, and then if he’s important and only at the end does he asks if “people” like him, which means that he asks the previous questions to John only, to know what he thought about him.

Yes, he knows he is human and he knows that John would say he is clever because no one else says that to him. And he knows people don’t like him but he’s OK with that because John just said he is important to him, and for Sherlock, that’s enough.