Heroes cannot use the same power two times in a single turn even if they are able to use multiple powers. Now if there two copies of the same card out, such as Tempest with two Cleansing Downpours, then he could use both of them if he has a way of activating a second power such as Embolden from Fanatic.
a. All Living Rockslides would act, so each would deal H-2 damage to all non-villain targets. So if two Living Rockslides were in play than the heroes would be dealt damage twice, once by each of them.
b) Her limbs are not considered part of her. And yes if you have multiple Mountainous Carapace's reduction do stack with Akash'Bhuta, so she would have a minus two damage dealt to her if there are two Carapace's in play.
OK so now I think I got it. you cannot activate the same power 2 times on 1 card but you can on multiples as long as they are not limited ( as you would only have 1).
Yeah, you can activate multiple copies of the same card but only if there's something allowing you to use an extra power during your power phase (eg Embolden, Flame Spike, Legacy Ring).
With the Mountainous Carapaces, if you have something that's gonna be taking out multiple limbs at the same time (eg End of Days, or a multi-target nuke that'll do enough damage to finish off more than one limb at once), it's a good idea to destroy any Carapaces first so that they aren't there to soak damage from any other limbs being destroyed on the same turn :). Say there are two Carapaces out and you deal enough damage to destroy both of them (plus other limbs), destroy one Carapace first. Akash'Bhuta will hit herself for one less damage than it says on the card because the other Carapace is soaking it (whereas the first Carapace has just been destroyed so she doesn't get to soak for that as well). Then destroy the other Carapace - now she has no soak so takes max damage for this, then max damage for any other limbs destroyed after that.
Our current record of most-damage-dealt-at-once is for using End of Days on Akash'Bhuta when she had the "By Any Means" bounty on her from Chrono Range (causing her to take +1 damage from everything). So she was hitting herself for +1 damage for every limb destroyed, and she had quite a lotof limbs out. And then of course we made sure the bounty was conveniently destroyed last. Total damage to Akash'Bhuta that turn? 103 :D.
Yep. It's an Ongoing which, at the start of the environment turn, destroys ever other card in play except for itself, character cards, and relics. Then it destroys itself. It's basically the same as Apostate's Apocalypse card. So both Fanatic and Apostate, in either case, would get to keep their stuff, as would Nightmist (well, her relics, not her ongoings if she had any out). Everyone else would be reduced to square one. Obviously everything in your hand would stay where it was, as cards in-hand aren't in play. But End of Days is a pretty good "oh shit we're about to die" emergency card if the villain and/or environment has a whole load of stuff out that you just need to get rid of before the end of the round. It works well against Voss's Forced Deployment (destroys the card, which brings out the Minions from the trash...who then promptly get inescapably destroyed as well) and though I haven't had a chance to do so yet, would probably be pretty handy if the Chairman or Citizen Dawn had got a whole load of guys out :).
Another way to maximise the End of Days damage against Akash'Bhuta (other than via that bounty) would be if you were Insula Primalis and had all three Obsidian Fields out. And if the Adept had used Syncopated Onslaught to give Akash'Bhuta a +1 damage dealt (obviously he'd probably only do this knowing that End of Days was about to take effect). There's probably a few other ways as well, but a well-placed End of Days can certainly be a game finisher :).