Droid is a trademark, owned my Lucasfilm, for which verizon pays licensing rights.

It would be up to the terms of the licensing agreement, but it is possible.

Probably not. While the Droid mark is a distinct trade mark, it seems to me that Google would have a compelling argument that calling a non-Android Droid would lead to confusion amongst consumers.

Additionally, although unlikely, it may be the case that the licence Verizon has been granted by Lucasfilm relates only to Android phones. As the licence agreement is not public, it's difficult to know whether this is the case or not.