both mean the same and are being used) However, "I do not work Monday mornings" is grammatically incorrect, since you need a preposition after the verb 'work" to clarify when. If you write an academic passage or an essay on a TOEFL, it would most certainly count as a mistake. But in a spoken English it is used quite often) As a sign of an negative attitude I think)

There's no difference in meaning. The 'on' is optional. The only difference is that the version without the preposition sounds more informal.