Both sentences 1 and 2 mean that you will definitely not be there on Monday or Tuesday.
In ‘b’, the word ‘on’ could be omitted ‘I might be here neither Monday nor Tuesday’ - though I would prefer to say ‘I might not be here on Monday or Tuesday’.
They are theoretically correct, but the meaning of 1 and 2 is slightly different from the sentences you had earlier. They suggest that you may be there on one of the days, but not both.
Sentence 3 suggests that it is questionable whether you will be there on either of the days. My sentence also means this, but is written in a more usual form.
The difference is the use of ‘Monday or Tuesday’ and ‘Monday and Tuesday’.