You can do this:

Quaternion rotation = Quaternion.Euler(x,y,z);
Vector3 myVector = Vector3.one;
Vector3 rotateVector = rotation * myVector;

It's important that the Quaternion is on the left side of the *.

Yes.

The preferred way is to use Quaternions. Conceptually (mathematically) they are a bit intimidating, but if you treat them as a black box that stores rotations, they are pretty easy.

See the first example in this forum thread to see how easy it is: http://forum.unity3d.com/viewtopic.php?p=303861

Here is a link to the documentation.