I STFW'd but I didn't find any answers to these logical fallacies or
the origin of the song.

Why are there 99 bottles of beer on the wall? Shouldn't they be in the
fridge or in a cooler? And why are they passing them around one at a
time? If they have 99 bottles then there's plenty enough for everybody
to have their own bottles and not have to share their germs - I'd sure
hate to be the guy at the tail end of the bar!