Originally Posted by Vizcaster
No actually the nut is one of the first things I like to address. Once the nut slots are properly cut, though, you probably never need to change it again.
Also for the OP's last question, a change in string gauge will require some setup adjustments, but don't go up a gauge because you expect the action to be different.
The Fender guide is probably one of the few places that recommends measurements at the 17th fret with a capo at the 1st. Most discussions of action height talk about the string height over the 12th fret without a capo.
The measurement given by Fender for relief is really huge. In inches, they recommend .010" but I usually wind up down at .006 or .007" So start at their spec and see if you're happier with less relief than that.
If you can't get the action low enough, and the saddles are already bottomed out, then unless something else is going on you would benefit from shimming the neck in order to get your action in the right neighborhood. Also, there's a side benefit from shimming the neck: if you can get the saddles sitting higher, then there's a more dramatic down angle behind the saddle and this can sometimes improve tone and the feel of the strings.
In the Fender manual, they recommend measuring string height at the 17th... but there is no mention of doing this with a capo on the first fret.
The capo is only indicated for setting relief.