The Mini itself should be OK. I'd check the power supply brick. In the past Apple have occasionally used 110V supplies for some desktop machines sold in the US. Without seeing the brick itself it's pretty much impossible to say.
Yeah, that's what I'd expect and hope for (basically a global supply). I just remember that some iMacs sold in the US a few years back had 110v ONLY power supplies. When people plugged them into UK outlets the power supply went up in a puff of smoke!