To answer your second question first, the time span depends upon the type of license you require. If you want a commercial license with multiengine and instrument ratings then you'll likely be resricted by how quickly you can build the minimum hours required (250).
In terms of G registered aircraft they are operating in the US every day, whether they be BA or Virgin and many others or corporate operations. For this you do not require an FAA license but a JAA license. You might wish to check out the FAA website for further clarification. As ever, depending on the type of operation, you may require a permit or approval of some sort in order conduct that. Please check with the FAA on this beforehand...