"got" is not required and feels pretty odd to this native speaker..... unless the "getting" was something active. So if you were playing a game as children and you were hunting your sister you might say "I have caught my sister" or "I have got my sister".

US - In most situations, I would say "I have a sister." That's the construction I would use if I were talking about my family or in answer to most questions. I might use "I have got a sister," if I really wanted to emphasize that fact. (If I was being interrogated or doubted or something.) It's not wrong, but it is a very strong sentence for a simple statement.

Same meaning. The "got" is common in British English, but not in America. Usually, we Brits would contract the "have" to give "I've got ..." Just to confuse you more, we don't generally ever use "gotten" in modern British English. It was more common in the past. I'm sorry, English doesn't make a lot of sense sometimes. :)