I'm having a hard time determining how this works even with the current FAQ and couldn't find a clear answer with a forum search. Is the only uncancellable damage that which specifically uses the word "uncancellable" like Counterstrike, meaning most non-combat damage sources can be cancelled even though there's no time between assigning and applying damage? For that matter, would the same apply to effects which happen in combat like Cauldron of Blood (which I'm not even sure if it's combat or non-combat damage)? Lastly, does the most recent War Hydra update in the FAQ mean it's damage cancellation applies to anything Toughness would apply to? Thanks.

The way I understand it is that the difference between combat and non-combat damage is that there is no action window between assign and apply for non-combat damage. That means you cannot play an action to cancel the damage before it is applied. But constant effects like keywords etc. can still cancel the damage, as they do not require an action window to be activated. So, non-combat damage can be cancelled, but the effect needs to be active before it happens.

Tako has it right, I'll just add to it that damage dealt during combat is not "combat damage" if its dealt by an effect. The only that that is combat damage is the 2 units hitting each other.

Also, yes, War Hydra now can occur just about whenever Toughness does. Toughness is still a constant effect, while the new Hydra is a Forced. The Hydra was changed because the old version could not cancel non-combat damage (because it was an action and there is no action window there).

Given that tactic effects are first in last out couldn't you cancel tactic based non-combat damage with High Elfs Disdain? ("action: cancel a tactic just played") Or am I thinking about this the wrong way?

That is correct, but strictly speaking you are canceling the tactic as a whole, not the damage it deals. Also, this would of ourcse take place during an action window, as otherwsie the tactic could not be played in the first place.