No, Azula had real character, and I’ve heard that they originally wanted her to have an arc similar to Zuko’s, but couldn’t work it in.
She’s not a true sociopath (though she like to play one on tv) because she does care; if Azula didn’t, she wouldn’t have been so hurt when Mai and Ty Lee turned on her. Sure, she could have been angry, but not knotted up inside, if she were completely bad.
Likewise, she could have eliminated Zuko cleanly and left herself as the sole heir. She didn’t, even though she desperately wanted Ozai’s approval. Azula actually handed Zuko the honors for it, brough him back to her family. Yes, she messed with him afterward, but even that didn’t really come to anything, and there’s little evidence to suggest that she was trying to undercut him otherwise.
Azula just can’t separate her love and her hate and her manipulation. She seems to enjoy poking and poking and poking at the people she loves. Meanwhile, she utterly adores Ozai, and her reaction to him is more akin to worship than familial love. And I don’t believe for an instant that Ozai didn’t deliberately create that. Note that Ozai rejects his son (like Azulon rejects him); he may have feared that Zuko would one day kill him.
Basically, when I see Azula, I see someone who is very, very much like Zuko… but with no Uncle Iroh to help show him the path. Nobody ever really cared about Azula… except her mother. Ozai viewed her as a disposable tool. Zuko could never entirely trust her. Only her mother .
On the subject of love, hate, and manipulation, note what Azula does as a child - she sees that Mai has a crush on Zuko. She puts an apple on Mai’s head, lights in on fire, and thus forces Zuko to . In one moment she demonstrates that she understands both of them very well, and simultaneously humiliates them and pushes them together. Later on, she has a delusion (probably) of Ursa, and sees Ursa saying what Azula knows she would say and what she wants Ursa to say… but she still can’t believe it.
Azula at her best is a classic “trickster” figure, who does good by doing a lot of evil (somehow). Her darker side is the domination of others, which to me reflects Ozai. From her mother, she has strength of will, deception, and desperation; from her father, hatred. Sure, she has her own personality, but she’s she’s just like Zuko - torn between her Father’s corruption and her Mother’s purity.
And Azula’s hatred is self-hatred, exactly like Zuko. Ozai pushed his evil outward, but both Zuko and Azula can’t do that. They know there is real good, so they internalize it. But neither one can contain that much anger, and so they lash out.
There is no explanation for Sparky Sparky Boom Man. Supposedfly he’s a super-specialized Fire Bender with a unique talent, although he acts more like a Boddhisatva of Destruction to me. He evidently blow off some of his own limbs and uses Firebending to work the cyborg parts or something.