2) If the Necromancer kills himself under the effects of Dark Charm does he regain 1 health point for killing a monster (Since Dark Charm says the hero attacks "as if he were a monster")?
I think that Steve-O's interpretation that the hero attacks as a monster, but does not count as a monster for other purposes, is probably the best one. In particular, if he counted as a monster for purposes of targeting, could he even attack himself in the first place? You normally can only target a space containing an enemy.
However, just for completeness, I'd like to offer another angle on this question. Suppose he does count as a monster, and therefore fulfills the triggering condition on his ability that lets him recover wounds…
Consider the order in which these effects resolve. Suppose, for a moment, that reactions are resolved after the thing that triggers them - that is, the order is: first defeat the target, then the necromancer can use his ability to recover 1 wound.
In this case, the necromancer cannot be healed for defeating himself because he would be knocked out at the time he would need to invoke his ability, and "a hero cannot use skills or abilities while knocked out, unless an effect specifically allows it." (Knocked Out rules, p.15) It doesn't matter whether he fulfills the condition of "defeating a monster", because the ability is no longer available. Even if he defeated a monster at the same time (e.g. with a Blast attack), he still couldn't heal.
Though, this order of resolution may be problematic for effects like "cancel a wound being dealt to you" (if 2e has effects like that) - do you need to resolve the wound first, before you can cancel it? That gets awkward…
On the other hand, suppose that effects resolve in a stack: once we determine that a creature is being defeated, the necromancer can invoke his ability, and then his ability is resolved before the target is defeated. So, first the necromancer recovers one wound. Then, we move down to the next effect in the stack - the necromancer's defeat. Do we resolve effects already in the stack even if the condition that caused them is no longer fulfilled? Intuitively, it seems to me that they must be - otherwise we reacted to something that never actually occurred. (And generally, in games, you only check a condition when you begin something - e.g. if you have a spell that temporarily turns a creature into a statue, it doesn't break early simply because the target is now a statue and is therefore no longer a valid target for the spell).
If the necromancer is still defeated after being healed, I think a strong argument can be made that this erases the healing. "When a hero is defeated, he immediately suffers fatigue up to his Stamina, and damage up to his Health (if defeated by some other effect)". Technically, the rules seem to say that he suffers damage up to his health only if the effect that defeated him was not damage, but I suspect that parenthetical was intended to explain to the player why that rule exists rather than to restrict its application.
However, even if it doesn't reverse the healing, the healing doesn't revive him, either, because he wasn't knocked out at the moment that the healing occurred. So he would effectively get an extra point of healing whenever he manages to get back up, but he would still be knocked out until something else brings him back.