#1
Right, so I'm an Avenged Sevenfold fan and imo, not being able to sweep pick very well is despicable. Can anyone give me any tips on how to get better?
#2
Practice. A lot. Start slow, and when you are comfortable, get faster.
#3
I practice with just sweeping different chord shapes. One you get them down, add hammer ons, pull offs, slides, etc.

I'm working on 5 string sweeps right now, and one of my favorite things is to sweep the A minor barre chord shape and to slide between chords on different strings.

LOTS OF PRACTICE! And slowly. Cannot stress this enough
I'll pretend I can mod your amp but break it instead.
#4
Practice. Sweeping is one of those skills that just clicks after a while. Once you "click", it's really easy to get to a respectable speed. Until then, practice the muting techniques and the sweeping motion along with incorporating sweeping into your skill set.