I don't know, but supposedly some of the Swan Necked Flasks from Pasteur's experiment survive to this day, and they are still microbe free. While an upside-down bottle is not quite the same thing, I would imagine you'd be okay for a while. Having said that, I (foil) cover and refrigerate mine after allowing them to drip dry for an hour or two.
I never leave them on the bottling tree for more than 20 minutes or so. Sanitize just before you start bottling. They may last longer, but why would you need to?
Yea. My method. I sanitize my bottling bucket along with racking cane, spoon, capper etc. Dunk my tree in it, Then drain from the bucket into the bottles sitting in a cooler. This also sanitizes the hose and spigot. Empty bottles, saving some sanitizer in a mason jar for the caps and airlock, and place on tree. Close cooler lid and use as a bottling table. Pour in priming sugar and rack to bucket. Bottle. Not sure why you would sanitize the bottles in advance unless you ran outa time.
Sanitize right before you bottle your batch. Don't fear the foam. It'll be the first thing that pushes out the top of the bottle anyway.