There is no difference in meaning. Both are correct, in spite of the fact that the apostrophe + 's' seems unnecessary/ superfluous. Both are commonly used: at least when talking about people. (So for example you would not say *"the legs of the table's"*, but: "the legs of the table".) Why can you say both? Well there is a lot of debate about that among grammarians - but no really conclusive answer. You can often find this type of 'double genitive', or 'double possessive' in English, going back to Shakespeare... 🙂

Charlie is correct. Both are acceptable and convey the same meaning: this man is friends with your father.

first is not correct, second is. "father's" is possessive. You could say "He is a friend of my father's boss". Or, "He is my father's friend".