In US English:
1. "Do you have meat" = "Are you in posession of meat."
2. "Have you gotten meat" = "Have you obtained meat."
3. "Have you got meat" could mean either of the above. But it is better (i.e., simpler, more elegant) to use 1 if that is what you mean. Certainly in writing you should use 1 rather than 3.
US English likes to use 'any' with it a lot. Do you have any meat. It's not usual to say obtained regarding groceries. You obtain a degree, a skill, "certain information about this person", but not, we obtained food. We 'picked up some food, some apples, some milk'. I think ion is using obtained just to make the grammatical point. In my life I have never heard or said, Hey mom did you obtain meat from the store, did you obtain roast, hotdogs, drinks or anything else. Hope that helps your English
I'm a native U.S. and Canadian English speaker and "gotten" isn't a word I hear used often in major cities on the northwestern coast of North America. It's generally considered bad English. Instead, we use alternatives like "received" or "picked up" or "arrived" (e.g., "We haven't arrived" vs. "We haven't gotten there"). Like many words in English, this probably comes down to regional differences.
Both, depending. did you get meat, did you get the meat darling? is very normal and so is I had gotten it before you texted me. Gotten is usually further past than got. So ... Yes, I got the meat could be any time in the past, maybe it's an old argument from 5 years ago you can still say No I got the meat, but when you say gotten it is used with the helping verb 'had' which using it that way, I had gotten the meat first like you said!, adds a lot of emphasis to it. But bad English would be to said "I had got (some) meat" and would be like a colloquialism that is improper but used and understood by certain people.