Hello.
If you get an unrestricted class 1, passing the CAD test for example, you have no limitations, you will be just like any other class 1 holder.
I did take the CAD test at City University and I was told to bring my results to CAA and that it would have been ok (unfortunately I can't be sure about this because I decided to do an Italian medical, but again that is what I was told).
For the last question, at the moment the CAD test is not recognised by EASA but I found out that it should be approved by the end of 2016.