#1
Okay, do such pedals exist? I once read in a guitar mag (Total Guitar, Feb '06, not sure though. It had a guitar lesson by Avenged Sevenfold in it...), where they were saying Avenged Sevenfold's dual-guitar harmonising sounds more like they're running a guitar through a harmoniser pedal...
#4
There are harmonizer pedals:

Boss HR-2
Boss PS-5
Boss PS-3

I used to have the HR-2, used it a lot when I was playing with a classic rock band. The PS-5 is Boss' latest harmonizer, which can be ran in series or parallel. Tracking really isn't too big of a problem with them, but don't expect it to track everything 100% if you try shredding at 200bpm.