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.
Idiomatically, it is gentleman. Lady comes from an Old English compound noun meaning roughly "loaf kneader," whereas lord comes from a compound noun meaning "loaf keeper" or "loaf protector." The etymological counterpart of gentleman, which is indeed gentlewoman, is used infrequently these days, usually in historical or quasi-historical contexts.
single word requests - Is there an opposite gender for "lady ...
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 ...
Yes, milady comes from "my lady". Milady (from my lady) is an English term of address to a noble woman. It is the female form of milord. And here's some background on milord: In the nineteenth century, milord (also milor) (pronounced "mee-lor") was well-known as a word which continental Europeans (especially French) whose jobs often brought them into contact with travellers (innkeepers, guides ...
These seats are reserved for ladies. The old lady running the roadside lunch house brought him rice and curry. The new District Collector is a lady. Calling somebody a 'woman' is usually perceived as rude here, with the notable exceptions of news journalism, law, bureaucratese and scientific literature: Bangalore woman wins Maths Olympiad.