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Hello. I feel that this could be too obvious, but here it goes. It's about short answers and comment tags with some modal verbs, but as I rarely hear or read these expressions I'd like to ask you if they sound awkward, are not used at all, or you avoid using them.

would you like to dance? yes, I would / no, I wouldn't
may she smoke? yes, she may / no, she may not
might I stay here? yes, you may / no, you may not
must we stop now? yes, we must / no, we must not
should I drive carefully? yes, you should / no, you shouldn't

he could find a job. Could he?
he would be a good athlete. Would he?
they shouldn't waste food. Shouldn't they?
he will be at the party. Will he?
he must be at home. Must he?
it might not happen. mightn't it?
he may come with us. mayn't he?
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All are fine as paradigms except: 'might I stay here? yes, you might / no, you might not '.

Having said that, in practice, many are uncommon tags, the response in real conversation being more likely 'why?/why not?', 'sure', 'of course', 'I'm afraid so/not', etc. Some-- like 'may not', 'must not' (which actually carries another meaning -- 'are not permitted'), 'might not' (which also suggests another more common meaning -- 'perhaps not')-- are so uncommon as to sound hyperformal or otherwise a little unusual.
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Hello, MrM.
1) About the second group of sentences (comment tags) which would it be the response in conversation to them? Something like this:

He could find a job. Really?
He would be a good athlete. No way.
They shouldn't waste food. I can't believe it.
He will be at the party. Sure?
It might not happen. Really?

2) Could you explain it more deeply the reason why this sentence is not correct?

might I stay here? yes, you might / no, you might not
(1) Yes, that's the kind of response I would expect to be as likely as a simple repeated tag. Both are possible, of course.

(2) Nothing wrong with those-- I had merely corrected your original, which reads: 'might I stay here? yes, you may / no, you may not'. However, the tag 'no, you might not' is one of those uncommon ones whose other meaning, 'no, perhaps you will not', is more expected than the simple negation, 'no, you are not permitted to'.
Tag and response? He mayn't play with grasshopper,
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