I am going to purchase a new car that is a left-over 2015. As that oil has been sitting there for over a year should they change it for me?

Not necessary. Your brand-new car probably only has a few miles on it and oil sitting in an engine does not "go bad" like milk left sitting out on the counter. Just for general principals, I WOULD recommend an oil and filter change at about HALF the time/distance recommended by the manufacturer for the FIRST oil change, but after that, just keep up with the manufacturer's recommended service intervals, and you should be good. (READ the owner's manual!)

No need, it'll be fine.

There's no guarantee that the oil they replace it with will be fresher than twelve months old anyway.

I would get an oil change thrown in.

No it will be fine.