Can a "a hero may use a power now" incapactiated ability cause an incapacitated hero to use the power printed on plauge rat's "filthy vermin" charected card, which says "infected heroes have these powers"?
I would say so, yes, because while Plague Rat is flipped to that side, all Infected heroes are said to consider those powers their own. It'd be the same with the Rod of Anubis and Idol of Anput treasure from the Tomb of Anubis - both grant their wielders the appropriate powers. It's just that in the case of Plague Rat, the powers are printed on his card, rather than on one you can have in your own play area.
Actually, I'm pretty sure incapacitated heroes can't use powers. They have incapacitated abilities they can use, but that's it. Even if Infection or another card gives them a power, they can't use it.
They can't do it on their own turn, but they might be able to do it on somebody else's. The rulebook doesn't explicitly say they can't.
Wow, I didn't even read the question properly, lol...yeah I suppose they wouldn't be able to use those powers on their own turn because once you're Incapaciteted, you don't get a Power phase (or a Play phase, or a Draw phase).
But what about if they have a "a hero may use a power" incapacitated ability
I don't think any of the incapacitated abilities are actually powers. For one thing, none of them have the Power keyword attached to them. You can use that ability on a hero who is alive and have them use a power, but I don't think you can use an incapacitated hero's ability to activate another incapacitated hero ability. I do believe that when a hero is defeated all their cards and cards attached them are considered blank and out of play.
No. They don't have powers. How would they use those abiltiies anyway? One heals them (impossible as they've got no hit points to heal) and one does them damsge (impossible as they're not targets). So, even if they had powers, which they don't as incapacitates heropes don't have powers, they couldn't use them.
I haven't. I pointed out why they couldn't use those abilties in my reply. Incapacitated heroes do not have powers. Not from their cards, not from Plague Rat not from the Tomb of Anubis relics, not from [REDATCED], they do not have powers. And even if they did, the ones from Plague Rat's flip side couldn't be used by them as they are not targets.
But plauge rat's flip-side abilities are powers, one of which it would make sense for a dead hero to use. "destroy a card named infection" Can you stop misunderstanding my question?
Plague rat's flipside powers. First of all, It has been stated in the rules that incapacitated heros can not heal, so the first power is rendered useless by that. A hero that has no HP, can not deal himself damage, which rules out the second power. The powers rely on the heroes being infected. When a hero dies all their cards become blank and are considered out of play. This would also apply to the Infection. It's kind of like when a hero dies, but they have Twist the Ether, the Twist the Ether goes away when they're defeated.
You can probably use an incapacitated ability to activate a plague power on a hero who still has HP and is infected.
Incapactitated heroes staying infected was officially ruled.
My question was using it on a dead infected hero.
And that's been answered. Repeatedly. the answer is no.
Pwatson1974, an ability that produces an effect that is impossible (aka damage to a non-target) does that mean that the ability could not be used. You could still use the "destroy a card named infection" or "your hero deals a hero target 3 toxic damage" piece.
A hero's power is printed on the the side of the card with the HP. The question is whether or not Powers given by an infection carry over to both sides of the hero card or just the side that has a power printed on it. I would assume no, because both powers produce impossible effects, which >G doesn't normally do, but you'll probably need an official ruling.
Keeping the infection card out at all produces an impossible effect ("At the start of that hero's turn, they deal themselves 1 irreducible toxic damage"). Plus there are alot of powers which produce impossible effects in certain situations, and those powers can still be used for their other effects.
I think it is reasonable to say that incapacitated heroes do not have a power phase to use the power directly, but if a card says they may use a power, I don't see why they couldn't.
Because… Christopher said so. 
Here's his response:
Incapacitated heroes cannot use powers, even if the villain or environment deck (Tomb of Anubis) grants them powers. Good question.
Personally, it makes thematic sense to me, as an incapacitated hero is down and not able to directly participate. (Their abilities are more about their loss motivating their companions and things like that.)
But that's just me. 
So...if a hero stays Infected even if they become Incapacitated, okay so they can't deal themselves the irreducible damage at the start of their turn because they have no hp. But would they still do Afflicted Frenzy damage, if that card was out? Or is an Incapacitated hero basically keeping an Infection card from Plague Rat's deck to no ill effect?