Isn't the two spaces thing a leftover from typewriting days when doing that made the typed text much easier to read? These days with word processing there's more control over the size of the gap, so I don't think it's that necessary. Depends on preference, I suppose, and your prof shouldn't penalise anyone for his personal preference unless the school has it in their rules for submission of assignments.

The Oxford comma I use off and on. I was told not to do it at school, but I can see that it has a place on occasion.