Anon asked: Azula offered to kill for Zuko in S&S? When? Kill whom? Even though I don't consider most of the comics canon, this particular idea seems very canonical to me. Azula knows that Zuko can be a 'softie' when he needs to be as ruthless as ever so she's like "You don't want to do this. I can tell. It's fine. I can do it for you"
Long, poorly written story short: Zuko fucked up mistreating his sister and then dragging her into a mission she should have not been a part of (at least not in her condition), Azula got worse and decided she wanted to help him out. She started out some chaos by kidnaping kids with her terrorist group made entirely of mentally ill teenage girls (good job, writers, nothing problematic or gross about that at all) so Zuko (who had been turned into a spineless idiot) would be forced to act. Obviously that put him in danger/made people question his authority a few times - in one of these times Azula was present and offered to kill the person who did it.
I wouldn't really call Zuko a "softie", but rather say that seeing both Katara and Aang deciding to show mercy to people who had wronged them (and in Aang's case, to the person who was still a very direct threat not just to him but to the whole world) and having proof that he should not use violence to resolve everything, he would be a bit hesitant to kill anyone unless it was for self-defense since, by that point, he'd be deeply aware that he relies on violence too much - just like he learned not to let his anger and pride get the best of him.
And while he would NOT be a door-mat like in the comics, hesitating, even if just for a while, could put in him danger, especially during his first years as ruler, when his political power still has not been solidified. And that's where Azula would come in. In the beginning of her redemption arc, when she is on Zuko's side but they still have some trouble seeing eye to eye, she'd be likely to act by herself, going against his explicit orders and "getting rid" of anyone who caused too much trouble (and she'll get away with disobeying the Fire Lord because that's her birth right as his younger sister).
But as their relationship evolves, they truly trust each other, and Zuko is a wiser ruler, she'd stop going against his wishes, and go back to being the "shoulder devil". One thing that was always fascinating about their relationship was how Azula would bait him or give him just a slight push towards the direction she wanted him to go, but let him choose for himself and do his thing. She'd be his advisor, and so he'd truly listen to her opinions, consider her points, tell her his own perspective and they'd decide together what would be the best course of action (and Azula would have about 5 back up plans, just in case things went wrong). Zuko would technically be the one in power, but anyone paying attention can see that Azula, who always understood politics much better than he did, is essentially ruling with him - like she said she would and should do in Smoke & Shadow.
It says a lot about just how important she is to make sure that Zuko succeeds as Fire Lord that even the comics didn't miss it.