#1
I have an Ibanez ART 320. I resently broke the nut where the low E sits. I brought it back to the guitar shop and had it replaced as it was still under warranty. I wasn't able to play it there. I put new strings on it at home (Super Slinks) and tuned it up. When I was putting the strings on it seemed like the nut was up too high. After I played it I know it's up too high as my pick wouldn't stay in between the 1st fret and the low E. Now when I play a F or A# power chord it just sounds sour, more so with distortion and less noticable when clean. To make the F sound good I actually have to flatten the tuning on the E. Higher up on the fret board the power chords sound fine. Intonation isn't perfect but all the strings are set fairly close to another at the 12th fret. Can the nut being too high cause this issue?

Also I have been having some fret buzz. (Even before the nut was changed). I checked the truss rod adjustment and the neck was just flat. I adjusted the truss rod. On this guitar they recomend .03 - .05 neck relief. I can get maybe .02 and the truss rod won't turn anymore. And no, I won't try to force it to turn more. So now to get rid of the buzzing I have to have the action set way too high for my preferance. Can this be an indication of a neck problem?

I bought the guitar new in April so it is still under warranty.

Either way I have the guitar in the car and will take it by the shop after work for a full set-up.
#2
sounds like the nut is definitely too high. when you tune the open string correctly it's taking a lot more downward movement to fret the string consequently taking it out of tune.

take it back, they need to shave some height off the nut. it should be easy enough to demonstrate the problem with the help of a chromatic tuner.
I've been imitated so well I've heard people copy my mistakes.
- Jimi Hendrix