In the US, ‘I’ve got a car’ is just a slightly shortened way to say ‘I have a car.’ You can’t substitute ‘gotten’ for ‘got’ without changing the meaning. ‘I’ve gotten’ in the US usually means ‘I’ve become’: I’ve gotten lazier as I’ve aged. Or ‘I’ve received’: I’ve gotten hundreds of emails asking for money. These uses of ‘get’ are natural and sometimes preferred in speech, but avoid them in writing or anything formal.

"Got" and "gotten" are both accepted as past participles of the verb "to get" and, as far as I know, this would be equally true in U.K. English. So "I have got something" and "I have gotten something" do not differ in any way. However, since "gotten" SOUNDS more like a participle than "got" does, you might want to use "gotten" whenever you want to emphasize role as a past participle. Since "got" is also simple past tense, the use of "gotten" disambiguates this double meaning. I recommend that you not ponder too much the verb "get". It is an imprecise word with thousands of meanings that seems almost to mean whatever a speaker might want it to mean. It occurs in hundreds of common expressions that make little sense if you try to analyze them. By all means, do use those expressions. They are colorful. But stick to just the idiomatic uses of "get" while you otherwise try to eliminate it from your vocabulary. Whenever you are tempted to use "get" outside of a common idiom, search for another word. You will ALWAYS find a better word than "get", and your vocabulary will improve as a result.

Yes! Great question. I have got your package here with me = present simple. I suppose got is not very experiential, so not the best verb to pair with present perfect, but as in your example, it's possible. Hope this helps.

What a fantastic question! Native English speaker here who lives in England, UK for over 50 years. In 'British' English, the word "gotten" is generally not used (I cannot remember ever hearing it in the way an American may use it). Instead, British English speakers typically use "got" as the past participle of "get." So, instead of saying "I've gotten two dogs," a British English speaker would say "I've got two dogs." However, there are exceptions used in England like "forgotten" or "ill-gotten", where "gotten" is part of the standard form. In believe as mentioned in American English, "gotten" is commonly used as the past participle of "get," so phrases like "I've gotten hundreds of emails" is okay American English. Just to clarify over here on this side of the pond, so-to-speak, we would say "I've received hundreds of emails".

"Have/has" and "have/has got" are interchangeable when we're talking about possessing something in the Present Simple tense: He has two brothers. He's got (has got) two brothers. We have three dogs. We have got three dos. This use of "have got" doesn't work with other meanings of "have" or in any other tense besides the Present Simple. For example, you can't use it instead of "having breakfast" or "having a good time." Just to add to the confusion, "got" is also be the Present Particle of "get" in British English (in American English, we use "gotten.") So in British English, you could hear "have/has got" used as the Present Perfect of "get" or as a variation of "have" or "has" to express possession in the Simple Present tense. You have to use the context to figure out which it is.