'None' would be used for saying there's a lack of something. 'No one' is more specifically referring to people.
So if you were talking about, for example, chairs, then you could say "There are none in the classroom". Or as said above if you were talking about students (if the topic was clear i.e. - the listener knows you are specifically referring to students) you could also use none.
In response to 'Is there anyone in the classroom?', it would be 'There is no one in the classroom'.
Sorry, I don't think this was a very clear explanation. >.<'