The cake I made will not fit in my fridge. I'm in the middle of making the frosting, but have not added any milk yet. I'm going to need some time to frost it, so I'm frosting it the night before serving it. In total, it will probably be unrefrigerated about 12 hours, probably even less than that. Is this okay? If not, should I use water instead of milk?

Yes, it can sit out as long as it isn't too hot/humid. No need to change from milk to water.

As long as the filling is shelf stable, you do not need to refrigerate American buttercreams.

I use milk and I do not refrigerate my cakes. There is a thread titled "icing" that I recommend that you read. Doug explains in great detail why it isn't necessary to refrigerate american buttercreams that are made with milk .

It's fine, something about the sugar mixing with the milk makes it stable.

Yes, it can sit out as long as it isn't too hot/humid. No need to change from milk to water.