when do we use and not use Apostrophe + s (for singular, uncountable, and irregular plural nouns) / Aposthrophe(for regular plural nouns) like the above examples?
when do we use independent possessive pronouns and nouns? only for things we possess? then why does this "The bag of an actress" sound correct as this is also a possession?
Very often, people indicate possession of, or association with, a thing by a person either with 'of' - the coat of my sister, or a possessive apostrophe and an 's' - my sister's coat. Either of these forms is fine for people, animals, concrete and abstract things: my father's hat/the hat of my father, my dog's tail/the tail of my dog, my car's engine/the engine of my car, England's coast/the coast of England.
Less usual, perhaps, but still valid in many contexts, and often useful, is the double possessive (or double genitive) where we use both - a friend of mine, a coat of my mother's, the bag of John's, an uncle of Jane's.
Sometimes, [...] English speakers will show the possession doubly, using two methods:
It had long been a dream of Mabel's to win the baking contest.
This kind of construction, known as the double possessive, or double genitive, dates back to Chaucer's time, and mostly gets used without being remarked upon by native speakers.
A Guide to Double Possessives (Merriam-Webster)
As Merriam-Webster says, there are plenty of people who will tell you that you mustn't do that. Suppose we re-write it?
It had long been a dream of Mabel to win the baking contest.
As M-W says, that is 'unidiomatic' and furthermore potentially confusing because 'a dream of Mabel' can make us think of a dream (by someone else) about Mabel. This points to one situation where a double possessive can be useful, namely to distinguish between possession and association (consider 'a picture of Joe/Joe's picture' and 'a picture of Joe's').
We can see that double possessives are often used for emphasis and clarification, but many native speakers use them naturally - Who was that woman you were talking to? She's a friend of my sister's. The general rule is to use them only about people or animals.
Keep in mind, as pointed out in Merriam-Webster's Dictionary of English Usage, that the "18th-century grammarians simply had a horror of anything double, because such constructions did not occur in Latin." But this is English, of course, not Latin, and despite its apparent redundancy, the double genitive is a well-established idiom—a functional part of the language dating back to Middle English. As Theodore Bernstein says in Miss Thistlebottom's Hobgoblins (1971), "the double genitive is of long standing, idiomatic, useful and here to stay."
