I've never used an edge 3 but here goes.
Ibanez guitars have very tall frets; if you push down on the strings there is a fair distance you can push it that will pull the string over the fret stretching it and raising the pitch. I've never heard of it going up a semi-tone, but it if its just a little bit it is kinda normal... Dunno what to suggest if it is a full semitone other then get smaller frets :S.
The thing where a note starts high and gets a bit flatter over time is a fact of life. I can't remember the physics behind it, but it's always there I'm pretty sure. It usually only happens if you hit the string pretty hard though, and is more noticable on larger strings. It's only noticeable at all on my low E, and the gauge shouldn't make too much difference. Maybe find a smaller block of wood if its changing the position of your blocked bridge too much.
The string buzzing could be a lot of things. Could be a loose part somewhere vibrating, could be the string touching other frets, could be a problem where the string touches the nut or the tremolo itself. Hard to say without looking at it. I would also suggest maybe checking out the profile of the curvature of your neck, it might be bending forwards or backwards a bit. It sounds to me like you should be taking it to a shop to have it looked at, as there are clearly lots of things to look at and I wouldn't reccomend going anywhere near a truss rod if you don't know what you're doing with it.
Just out of interest, sounds like you can't be arsed with the problems tremolos can be (they can be bloody annoying I'll grant you). Why not get a hardtail if you've ended up just blocking the trem anyway? Unless you're really into whammy tricks (like me, woo) even I don't think they're worth the bother.
EDIT: wut neko says too, but bear in mind that can be a BITCH to adjust on some Ibanez trems, dunno about the edge 3.