The rules for RF specifically state that when the d10 rolled for damage has a "10" on its face is when you threaten Righteous Fury. (so this answers the d5 weapon question)
For multiple d10 weapons, you still only roll to confirm once for any distinct hit (full auto weapons are scary for this, as each of those hits could possibly cause a Righteous Fury).
For NPCs, as stated earlier, its mainly on for the Big Bads. Technically, its anyone who has the "Touched By The Fates" trait, which gives them Fate Points.
As far as psychic powers, I'm in a minority here, but I recognize that RAW in the book they do not, but that some developers have answered rules questions saying that they do (with a confirmation roll of whatever it takes to manifest the power).
The reason I say they do not is specifically because the RF rules state you only threaten RF as a result of any damage that came about from an attack made using a WS or BS roll. Not a power manifestation, not an opposed Willpower test (looking at force weapons). Personally I feel they do enough damage anyway that they don't really need RF. Once again though, most people are going to say this does threaten Righteous Fury, and they're not necessarily wrong.