It's interesting to note that the songs continue in America today, even if they may be subject to cultural/regional change. I don't know if Ring around the Rosie is an American change or maybe it has been imported by people who may have said the rhyme differently in another region of the UK. That said, I do know that "Ladybird" is a translation of "Ladybug."

No idea if the Pussycat rhyme means anything, though I did hear a rumour that Humpty Dumpty is about mad King George. "All the king's horses and all the king's men" is supposed to represent the courtiers who tried every means of "curing" him, to no avail. Well, so I heard. The Grand Old Duke of York was about another madman. English history! Full of crazy people!