It probably has to do with the phonetic and metrical properties of "ladies and gentlemen" versus "gentlemen and ladies." Say them both out loud and see which one sounds better to you, intuitively.
Ladies and gentlemen everyone [nothing] friends / folks / team Avoid mixing and matching: both hey there, ladies and gentlemen, let's rock! and S'up, honoured guests? are kind of weird. Not impossible to use, but definitely an expert technique. It's fine to say Good morning folks though.
I don't know why you might think Ladies and gentlemen as a form of address started in America. The capitalisation of this NGram chart means it will mostly pick up contexts where it's used to address the group collectively, and if anything it seems to have started to gain traction in BrE, not AmE. But in any case, I'm sure it was always used for all mixed-sex audiences, not just the nobility.
The plural possessive is "ladies'." "Lady" is singular, so if you were referring solely to one woman's shoes, it would be "the lady's shoes." As for your second question, I'm assuming you're referring to a group of women in your salutation of them, so it would be "Good morning, ladies." And as you're addressing them directly, the comma preceding "ladies" is necessary.
Hence, there is no ambiguity with the men, and for the same reason no ambiguity with the ladies. Ladies is the plural form of lady, so the apostrophe goes to the right - ladies'. If you are wondering why we don't write ladies's, it is because ladies is one of the exceptions, along with girls', parents', players', weeks' and even Klingons'