Death's Oath aura mechanics

Hello,

I'm following one of the builds[1] based around the aura skill provided by Death's Oath and it's proving difficult for me to understand how the aura works and how to further improve my output. It would be really appreciated if some experienced players could answer a few questions I have.

Q1. For an aura skill like Death Auth, what's the difference between DPS shown on the tooltip versus "Damage Per Use" in the Offence panel?

Q2. Is Death Aura tagged as a "Spell"? Either way, is there an official way to know which tags a spell has?

I ask because the new abyss jewels have a modifier "Adds X to Y Chaos Damage to Spells" which seems to have an effect in the "Offence" panel statistics for the skill but NOT in the tooltip (nor in POB, for the matter.)

If the "to Spells" part makes it inapplicable I'd rather know before spending more currency.

Here is an explanation in screenshots. First, the item without any flat Chaos damage added (to Spells or not):



Now, let's put on some abyss jewels:



Is this actually benefitting the damage at all?

Q3. "Flat" chaos damage, such as provided by Malachai's Vision Praetor Crown - is it added to the DoT?

This may be related to the answer of Q2 because it exhibits the same behaviour; the tooltip DPS is not affected but the values in the Offence panel increase when I wear the helm.

Thanks.

[1] https://www.pathofexile.com/forum/view-thread/1987659

Thank you so much. That clears it up.

Perhaps it's worth linking your answer to that build guide because Malachai's helm costs so much especially since it's corrupted and since it doesn't actually benefit the DPS of Death Aura, there are better ES choices out there.