I live in NJ and am remodeling a bath. Can I run my supply lines to the shower in an outside wall? If so any recommendations or hints concerning this?

First I must tell you I am not aware of New Jersey special building codes and second I must tell you that the supply lines must conform to your local building code. To find out what your local building code allows ask a building inspector or someone at your local plumbing store. But to answer your question simply, Yes. I will say that I am assuming you are using copper pipe and that you will solder your pipe to the shower fixture or that you will solder the pipe to an adapter that will screw to the shower fixture.

I am not sure of the codes but will check. Yes, yes and yes to the copper