Okay, when determining whether or not the Disciple's ability triggers there are really only three things you have to look for.
1) Was it cast or revealed by your Mage? All enchantments are revealed by your mage, so really this only applies when looking at things being cast.
2) Is it a spell? The ability on Faith Healer's Staff never mentions it counting as a spell, so it is not. Resplendent Bow is an attack and not a spell.
3) Does it have the Healing subtype? It doesn't matter if it provides healing or not. It matters if it has the healing subtype. The Priestess's Restore ability counts as a spell, but doesn't have the Healing subtype.
Something would have to get a yes to all three of these criteria to trigger the Disciple of Radiance. None of your questions pass that test.
Now, a question that I'm not sure of is whether or not the healing subtype is being represented by iconography on some spells. I think it is. If you look up Heal in the Codex, you'll see an icon of a hand with light shining out of it. This icon can be found on some cards like [mwcard=DNQ09]Wand of Healing[/mwcard]. I believe this indicates that they count as Healing spells and would trigger Disciple of Radiance, but I'm not positive.
