Chaos Scrolls

Oh, and that leaves me with another question: Is there a chance of having the chaos scroll not affecting anything at all? That is, the scroll works, but gives the same as a failing scroll.

Yes. Back during the leaf event with the maple syrups...
(if you didn't know what that was, the leaf was a face accessory that gives +5 of a certain stat (str, dex, int, luk) clean and the maple syrups were 100% chaos scrolls that worked exclusively on the leaves)
There were many instances when you could use the maple syrup and get the same stats out.

That being said, during the event, out of curiosity, I bought 70% hp scrolls and scrolled my leaves with them before hitting them with maple syrups. One of the leaves ended up the same hp AND same int after using a syrup. (That is, 15hp and 5int.) That only happened once though so it is a rare event. I'm pretty sure you'll ALMOST never get such a result with an item that has 7 different stats such as a HTP.

I wouldn't assume they're equally likely, it definitely seems to favour the -2 to +2 range (specifically +1 to +2).

They're definitely not. I'd say it's a bell curve from 0~5, with 2 being the top of the curve. (That is, 2 occurs most likely, then 1 or 3, then 4 or 0, then 5 being the lowest).