I've spent the last year tutoring English in college to both native English speakers who have been through the North American school system, and ESL students from a variety of countries.
What I've learned is that native English speakers don't always know even basic shit, other languages don't always have things like articles and apostrophes (and they get along fine,) and there are actually two forms of English that are equally valid: spoken and written.
When we speak "sisters'" and "sister's" it sounds exactly the same. The meaning is different, but the choice of meaning is provided by the context of the rest of the sentence. The neat thing about spoken language is that if the meaning isn't clear, we can see the puzzlement on the other person's face and clarify our statement.
Written language needs proper grammar and punctuation because we don't have things like tone of voice, hand gestures, facial expression, and body language to provide context; as well, we do not have the opportunity to address confusion in the listener.
There is a somewhat famous story about a legal contract that had millions of dollars at stake because of the placement of a comma. The legal issue was decided because, fortunately, the contract was also written in French, so the intended meaning was clear. Without the bilingual contract, one side may have lost the case unfairly because of the comma.
Precision of written language is essential for contracts, legislation, instruction manuals, and most internet posts that are subject to criticism by grammar Nazis. Grammar is not rocket science, and most native English speakers that have had at least some success in the educational system should be able to express themselves through writing in a coherent manner. If they can't, let's not blame the education system. The adults who are attempting to write have at least some responsibility to do so in a manner that provides meaning consistent with generations of language usage. If they are unable, they have at least some responsibility to seek help, or to STFU.
Addressing the OP's examples, yes, the first two are valid and the last is simply wrong, for reasons stated. What I appreciate is the connection that the OP is making to grammar and logic. Good grammar is an expression of logical thought. Similarly to mathematics, grammar and punctuation allow the expression of precise facts, and connect them in precise ways. The last example, "One of my sister's friend is an actress" is wrong because "One of" requires multiple possibilities, and "friend" is only one possibility. The statement isn't just grammatically incorrect, it is logically and mathematically incorrect. Proper use of language catches such errors, but more importantly, thinking in proper language forms prevents us from making such logical errors.