Basic combat situations don't count with the One Power. Guns can't tie people up just as fast as Setting Them On Fire.
Why is this specific to this situation, from you? Where was your outrage at Rand flinging fire and destruction at the Shaido in tFoH, instead of just trapping them in Air? We know that at that point, he could trap multiple people in a single web of Air, and also make walls of Air. Yet there he was, burning off entire hilltops. The Shaido surely deserve as much consideration as Sul'dam, right?
How? She knew they had one a'dam on them at least. But anyway... the point is meaningless. Even IF they had bombs in their pockets, it is irrelevant to this conversation, since, as you reminded us, this is the OP we are discussing.
In a combat situation, tying them up with Air, then having them transported somewhere safe would add to the danger to herself and her followers, since she needs everyone focussed on repelling the Seanchan. Unlike the Damane, the Sul'dam are NOT going to be passive and too scared to take initiative as a rule.
Depends on the Damane, and Egwene seems aware of the risk:
I still find it inexplicable that she didn't shield them. She had way more OP than them, and could have had them shielded in seconds. Just bad writing that she doesn't do so.
The same was true, to a much much greater extent, for Rand from a distance in Cairhein. He was too far for any Shaido bow to reach, and he was positioned to make them helpless and no threat to anyone. Yet he chose to kill them.
Again, rules made up in a complete different world, where the One Power does not exist, and thus does not need to be accounted for.
And your repudiation of these rules for Egwene alone, as if she is the sole channeler we have ever met, is indicative of your continuing bias.
I find it not at all surprising that only for Egwene, it is "cruel murder".
I can't recall the time the Aes Sedai raided the Whitecloak stronghold, or threatened them in any way physically. If they had, I would have zero issues with Whitecloaks shooting them from hiding.
And if Egwene Traveled to some random place and killed some random sul'dam the way she did the two who were part of an attack, I would condemn her for it.
Aes Sedai are not regular channelers, though. They explicitly cannot go on the offensive against anyone like a Whitecloak. Thus, the Whitecloak has an option with them... namely of not attacking.
That Perrin scene was moronic, though it involved ropes, if I recall. Branon's justification that she meant to transport him somewhere safe works, I guess, but that should really have been part of the scene if so. Either way, doing so takes Egwene away from the fight, which is something she would certainly not mind risking for her friend, but why she would do that for someone who is actually attacking her is beyond me.
So much time? Pre-Sanderson, she told them once that she meant them to take it despite the new info on them reducing lifespan, as far as I recall. And I don't ever remember her saying that was because of some deep belief in non-violence. Siuan convinced Egwene that the Oaths were politically important for Aes Sedai. And even then, Egwene specifically worried about the Seanchan as a hole in Siuan's argument.
Which is why I don't recall her telling them they need to be honest, or that they need to be less violent. That would be hypocritical of her. She wants them to take the Oaths to become Aes Sedai, because she has come to agree that the political benefits Siuan listed were too great to let the Oaths go completely. They hold as a common thread among the various Ajahs, and makes them a cohesive unit. And it makes a direct statement from an Aes Sedai impossible to ignore, which is a HUGE advantage. And the political powers of the land, and even commoners, can know that they are safe from physical assault using the OP, yet another huge advantage.
These are the things that convince Egwene. Siuan's argument is not that "being honest" and "being non-violent at (almost) all costs" are good things! And never is that something Egwene preaches to Elayne or Nynaeve. In fact, she specifically says:
And she also plans for Aes Sedai to retire by giving up the Oaths. Does that mean she thinks Kinswomen are inherently liars and violent? No. Does that mean she thinks they can do those things with impunity? No. But they will no longer have the benefit of implicit trust that their direct statements are true and that they physically cannot start violence against someone who doesn't threaten them. And they have to live with that, for half their lives at least, and Egwene is just fine with that because she came up with the plan herself.
All Egwene cares about is that women who want to be called Aes Sedai swear the Oaths. And that women have already been named Aes Sedai try live by them. I think it is beyond absurd to claim the Oaths would have held Egwene back from attacking the Sul'dam when we have seen, in similar situations, bound Aes Sedai do as much or more.
And since Egwene hasn't espoused non-violence as a way of life to anyone... what exactly is the hypocrisy here?
That Egwene has used the OP for violence in combat? I don't think anyone is arguing that. But you are implying she did murder, a whole other thing. And that is just flat out wrong.