How could they not have noticed a man with a knife, while they were holding the Power? That is much different than a weapon whose stealth capabilities it's weilder boasts of in that very room. You really need some sort of evidence that a man with a knife could have done anything at all. To assume he would have been successful as someone with an ranged energy discharge weapon is absurd.

In the first place, did you READ the book? No one was in the building! Or if they were in there, they were hiding! This is not some video game where the bad guys wait in their room, insensible to people downstairs tearing the place apart looking for power-ups or hidden enemies! A Warder checked the place out and said the coast was clear. What more do you want? The only reason you think there was insufficient checking is purely hindsight. And what on earth do you mean by "effectively alone"? She had three people with her, and they had to watch (potentially) three Darkfriends who were conferring in one room. There were two Aes Sedai, and Shiane. Elayne had already ordered Hanlon/Mellar's arrest, and Jaem secured the thug before they went in. There was no one else in Shiane's cell.

She couldn't as ANYONE who read the books would know! So why bring it up? As far as the Warders went, there were Careane's three Warders, while the good sisters had a geezer, a youth and a woman. In close combat, they'd be lucky to kill one of Careane's before they all died. I don't know what other book series you are reading where Elayne A. could have relied on help from Rand or B. could have even obtained it! She did not know where he was or what he was doing. Every word that Aviendha said about why they could not go to him at the Cleansing still applied! The situation was unchanged. She didn't know if she would be diverting him in a fight, if he might strike out before he realized it was her, or if she might spoil whatever he was up to by dropping in.

Oh, get real! How is she supposed to identify a thump of bootsteps from a thump of a bodies hitting the ground? She already commented on how much noise they make walking earlier in the book. And if she DID hear, and DID decide to do something - what could she have done? Been zapped on the stairs going down, instead of the upper room? Under ideal conditions the guards would have given her a second or two, and not have told her anything that could have prevented the exact same outcome. She had no idea what their weapon was, or if any counter for its effect exists. How could she have stopped it?

Your suggestions would not have changed the outcome one bit, would not have spared one life (aside from maybe Careanne's or Asne's if the takedowns had gone a little differently) that was lost that day, and only resulted in fewer bodyguards to protect the future queen. And the good guys HAVE to take risks, since they are on the short end. If they try to play it safe and conventional the whole way, they are going to lose to the superior numbers and raw power of the bad guys. Elayne had to gamble herself to get stuff done, in the same way Rand has to repeatedly risk the entire cause of the Light by going in harm's way to fight the Forsaken.

Except Elayne has not. Not only that, she took a situation where all of Birgitte's experience and her bodyguard's caution were telling them to get her back safely to the Palace, and insisted on a course of action that enabled her to win her war in one stroke. When wise old experienced Dyelin & Birgitte of the hundreds of lives were balking at her plans and preparations in the prologue to Winter's Heart, SHE turned out to have been right! Had she listened to their "experience" she would have been facing the beseigers with hardly any soldiers to contest the city. She was able to pick up on the idea of using gateways tactically, like, oh, Gareth Bryne, who's only the greatest military mind of her country.