No, there isn't. My experience with the train has been that it is not on schedule, so public transportation left me abandoned at the depot. There were no rental agencies open and I was stuck. Uber is the best solution.
Very close. Much closer than downtown and there is a bus stop out front that can take you to campus. Don't try parking on campus unless you have a parking permit. I would guess a mile from campus. From the Peach Tree, go a block towards downtown and go right on Grand, take that all the way to campus.