Anon asked: At what possible moments could have Azula killed her father as a way to protect/avenge her brother from/for his banishment? Of course, I also need some Zucest developments, if you would be so kind.
When it comes to protecting him from his banishment, maybe she overheard Ozai's plan on eavesdropped on his conversation with the general that Zuko thought would be the one to fight him. Both in that scenario and in a "is too late" one, it'd be like that really famous "Azula kills Ozai for Zuko" art, with her killing him with lightning, and having Iroh covering up for her. In a more public death type of thing, she'd kill her father either just as he's about to burn Zuko, or a second after he did it (bonus if it's the first time she is able to generate lightning). In all of these, Azula would realize she is in love with her brother the very moment she decides she's willing to do anything to protect him, and Zuko would realize his own feelings once he finds out what she did.
Another possibility is for her to understand/accept her feelings for Zuko when he was already banished, so when Ozai commands her to go capture him, she pulls an Ursa and kills him to protect Zuko. She becomes Fire Lord and goes after her Zuzu, who'd go home and fall in love with her.
If it happened post conquest of Ba Sing Se, they could start having a secret romance (likely after The Beach) and seeing how devoted she is to him now, Zuko tells her he is leaving their nation to join the Avatar and begs her to come with him. Azula tells him she needs to think it over first. The next morning, Ozai is dead and suddenly the invasion is no longer necessary, 'cos Fire Lord Zuko and Fire Lady Azula will make peace with the Avatar and the world.
Finally, if everything played out the way it did in the show, but Zuko tried helping Azula heal after her breakdown, they'd fall in love and she could escape the hospital/palace, sneak into the prison and kill Ozai as proof of her undying loyalty to Zuko. They'd get married as soon as possible.