I attack Patrol Leader with 2 Dwarrowdelf Axes. First of all I am assuming that the damage from the attack is seperate from the "after the attack" damage and thus require seperate discards to see if the damage is canceled. But with two Dwarrowdelf axes, do their "after the attack" damage resolve seperately from each other and require seperate card discards as well?

The normal ruling for things like this is, you decide in which order these effects happen. I have not heard of any situations where you can decide to do things 'at the same time'. Therefore, I would play it as 2 seperate actions/responses and would have to try for cancellation for each. It is a nice catch though. If you could decide to do the responses simultaneously, would you prefer 1 x ?% of 2/0 damage, or 2 x ?% of 1/0 damage each? I suspect it would depend on what ?% is and how much more damage you need to kill the Patrol Leader. However, I believe that as things stand, they have to be seperate savings. Cheers!

Rashley's correct. There's the "framework dealing damage" part, which is just part of normal combat resolution, and the Leader's Forced effect triggers. Then players can trigger responses, and the Leader's Forced effect triggers off of each of the Axes' Responses.

So there will, in effect, be 3 chunks of damage that Patrol Leader will try to cancel.

Rashley is further correct by saying that there are never any effects that happen "at the same time" in this game.