1. Survival Instincts prevents the "first 4 damage" of the round. Let's pretend you have multiple Survival Instincts, and someone uses Myriam. 4 points of damage are prevented as they are the "first 4"; and then 1 more is done - does this 1 now count as the "first damage" done, or do they all try to prevent ONLY the original "first 4"? In other words - if you have 4 Survival Instincts out, do you prevent 16 damage each turn?
They only count the original first four damage. Multiple Survival Instincts in play will not have any extra effect. Additionally, if you play it after damage has already been dealt that turn, that will be counted as the first four(assuming four or more damage was dealt) and it won't do anything for the remainder of the turn.
2. Let's say you have Power Word: Shield on your hero. Your opponent uses Myriam for five damage, but then you play Power Word: Shield, again, on your hero. Do both of the Power Word: Shields disappear as both try to prevent the damage, or only one of them? Do you get to choose which one is destroyed first if only one goes?
Only one will go, and you choose which one. Once the first one prevents all the damage, there is no more damage for the second one to prevent.
3. You have Xanata in play, and your opponent has Arcanium Bracers (double damage that target ally would take this turn - not sure if that was correct spelling). Your opponent attacks Xanata with Vexmaster Nar'jo (assuming that Xanata is ready). Xanata prevents the first 2 points of combat damage but your opponent has used Arcanium Bracers already on Xanata. Does she take 6 points of damage, and prevent 2, therefore taking 4 (and dying), or does she take 3 points, prevent 2, and then double the 1 remaining damage to 2 points?
All damage increasing replacement modifiers apply before damage preventing modifiers apply. So first his damage would be increased, and then two of that would be prevented.
4. Armor can only prevent damage as it is being dealt, so someone whose armor is "Smashed" cannot prevent the damage that results from Smash, correct?
Correct. First the equipment is destroyed, and then the damage is dealt. So if it was a piece of armor that was destroyed, it won't be around when the damage is being dealt.
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Sweet Zombie Uther!
It's a dirty job, but someone has to do it.