É errado dizer "the sister of Karen is my friend" ao invés de usar "Karen’s sister is my friend" ?

Nobody would say "sister of karen". Technically it's not gramatically incorrect, but nobody uses such structure in informal day-to-day language. Even in otherwise formal settings it's quite unheard of these days i'd say. That is, in that specific context anf type of sentence. It's normal and ok to say "the house of the Johnson family", for instance. But "the sister of karen is my friend" sounds way off.