As far as I am aware there is no comprehensive guide on this, it also doesn't help that in relation to CP it's not always super clear and ZOS hasn't helped much with clarification or cleaning up tool tips.

Attributes will effect any skills which require that attribute, unless stated otherwise.

Direct damage is any hit which isn't part of a damage over time (some DoT's have a direct damage hit to start)
Damage of Time is anything which ticks damage over time (with ESO damage pop-ups this is orange damage numbers)
Physical damage is anything which lands from a martial weapon or some stamina abilities.
Magic damage is anything which comes from a magicka attack but isn't an element.
Elemental damage is any of the elements.
Oblivion damage is not buffed or modified by any source.

Shock staff heavy attack is a DoT, correct.

Wall of elements should get benefits from Spell Power, Magicka, Element damage and DoT yes, I don't know if the initial hit is direct damage or not as it's not a targeted ability.

Sadly this isn't my expert area, I know some information but don't feel comfortable enough to give you solid answers as I don't want to spread any misinformation. Hopefully someone smarter than I can chime in though.