Are Mary Magdalene, Mary of Bethany, the woman caught in adultery, and the woman who anointed Jesus's feet the same or different women?

I do cover that in the Luke commentary, so you will have to go read it, because I cannot remember all the detail. Mary was a very common name then, and I would say, without even looking it up right now, that the four you mentioned are different women. For instance, the woman who anointed Jesus's feet in Luke is not necessarily Mary Magdalene; there is a lot of evidence that it is someone else. So that is one possibility, but I did detailed work on that in the commentary, so go read it for your answer.