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.
I tried searching Google Ngram Viewer for "Look lady" and "Listen lady", both capitalized so as to occur at the start of a sentence, with the hope that these ngrams would reflect the usage of "lady" in a derogatory/dismissive sense. It seems to have come into usage around 1950, and really took off in the late 1990s.
etymology - "Look, lady", "Listen, lady" – lady as a pejorative ...
single word requests - Is there an opposite gender for "lady ...
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' It can get a bit niggly with names too. Aristophanes' plays, but Jesus's miracles and (usually) James ...
Though, part grand lady, part wild child can also be fronted, so may simply be a supplement to the whole clause she was a curious mixture. Part grand lady, part wild child, she was a curious mixture. "Part grand lady, part wild child" is an adjunct. Yes, supplements are always adjuncts.
"She was a curious mixture, part grand lady, part wild child." — Is ...
The "fat lady" is the valkyrie Brünnhilde, who is traditionally presented as a very buxom lady with horned helmet, spear and round shield (although Amalie Materna played Brünnhilde during Wagner's lifetime (1876) with a winged helmet).