NO. not directly under the eyes where you would apply eye cream.

I live in USA and carry a converter with me when travelling and have not had any problems. Sometimes electronics do not last as long when using a converter plug but the Clarisonic is wonderful.

Yes, use it exactly the same as the original NuFace. Current is pretty much the same intensity.
What is different:
It does not use batteries. It sits on a cradle and is rechargeable, electrical outlet required.
It has a removable head, easier to clean. I've read other attachments may become available but no idea for what use yet.
It has a timer, beeps, to let you know how long to move it along the area.
Ergonomic, easier to hold.
You can reduce the intensity if you wish, but if you apply gel you shouldn't feel it at the highest intensity which is best.
New conductivity gel is available, paraben free, however I use aloe vera gel which I find lasts longer. The gel that is sold with it seems to dry up fast and is expensive.