I'm not sure people often say, "I live in the middle of the US" or "I live in the center of the US," but the meaning is clear. You could also say "I live in Central America," but this has a totally different meaning -- it means you live in Guatemala, Costa Rica, Panama, etc. Some common names for regions of the US are: the East coast, the West coast, the South, the Southeast, the Southwest, the Northwest, the Northeast (or New England), and the Midwest. The Midwest is basically in the center of the US. People also talk about living in "Middle America" or "the Heartland," but these terms mean more than just the center of the US. They also refer to a lifestyle and view of the world that people associate with the Midwest.

1) i live in the middle of Germany(could be any countries) This one is vague. It will solicit further questioning, like "What do you mean?" 2) I live in the center of Germany ( Could be any countries) Alright, but nobody knows where the center of Germany is. And it could mean financial center, cultural center, historical center, etc. So it's a bit vague. Sorry to bug you, but the correct phrases are: I live in Central Germany. I live in the central part of Germany.