According to the MINI website, and a window sticker I saw on one of the cars at the dealer, they are assembled at the BMW Group Plant in Oxford UK. The parts configuration was something like 18% german, a very low amount US and the rest UK.
I'd have to check, but it's likely that the Z4's are made at the Oxford plant as well, and I know for a fact they Charleston is one of the ports of entry for the MINI.
Once your order is placed for your MINI, you get the VIN and some other tracking number. You can track it's birth on the MINI website throughout production, and then you can find out what ship it's been placed on, and via some other website you can track the location of that ship while it crosses the Atlantic (and on through the Panama Canal if your car is being delivered to CA). These folks on one of the online forums that I've been lurking at are way further off the deep end than we are!
Specifically the one we're looking at is the MINI Cooper S with the John Cooper Works kit, which bumps the horsepower up to 207 with a better supercharge and air intake, better suspension, and upgraded exhaust with less backpressure. It will actually be my wife's Spring/summer/fall fun car, then it won't see many miles during the winter.