Can the adjective "absent" which has a negative meaning to it be used with the phrase "there is" or "there are" as, in their affirmative form, these are meant to assert the presence and not the absence of something or someone? Then is it correct for a teacher checking out the attendance of their pupils to ask their class: "Is any pupil/student absent/away today?". To which the class would answer either: "Yes miss, everyone's here today." or "No miss, everyone's not here today." Besides, is "Everyone's not here today." preferable to "No miss, not everyone is here today."?
"Yes miss, everyone is here today." or "No miss, everyone is not here today."
Both sentences above are answers to the question
"Is everyone present today?" or "Is everyone here today?"
They are not proper answers to the question
"Is any student absent today?"
To which, the appropriate answer would be
"Yes miss, Carla is absent. She is sick."
Honestly, I have never heard anyone answer the question "Is anyone absent today?" with "Yes miss, everyone is here today." I believe that would be quite strange.
It is like asking "How is everyone doing today?" and having students reply "Yes miss, no one is ill today." I suppose it could be used sarcastically.
The question is grammatically correct, but the teacher would be more likely to say
Is anybody absent/away today?
The yes/no part of your proposed answers is not correct, though. If nobody is absent, the students would answer "no" to the teacher's question:
No miss, everyone is here today
There are additional problems with your answers when one or more students are absent
Everyone's not here today
This is grammatically correct but logically incorrect- it would mean that nobody is here today.
Not everyone is here today
This is grammatically and logically correct, but not natural: a student would be more likely to say
Yes miss, X is absent today
Yes miss, some students are absent.