Both of them have comparable AP, but Shoto's ice attacks are slower than his regular reaction speed, which would allow Azula to easily dodge his ice attacks. Even if Shoto trapped Azula with his ice, Azula could use her firebending to evaporate the ice, as she's been shown to easily evaporate Katara's large waterbending attacks. Azula's firebending attacks are also extremely precise due to using her two fingers instead of just her fists. Honestly, I believe Azula would win this one. She's just got much greater skill and techniques at her disposal, and I think that after finding an opening, she's eventually finish Shoto with her lightning or one of her advanced firebending techniques.
A. Shouto’s durability scales to 5%, I.E 5.13 tons.
B. No she can’t melt the ice Firebending requires breathing and motion to work, in fact, the very same bender you mentioned trapped Azula in a coffin of ice that she couldn’t break free of. If Shouto Leads with the heaven piercing ice wall (which he will in a serious fight, a Standard Assumptions so he is) then all that needs to happen is that she gets hit, as seen against Nomu, his ice causes necrosis, game over for any body part it hits in a fight he’s willing to kill in.
C. This is season 2 Azula, she would have less skill then her final version, and even that wouldn’t compare to any of the stuff Endeavour put him through at a young age, and he was able to keep up with stain, sure he didn’t land hits, but he’s the only one out of him Deku and Iida to never be paralyzed, even when he had blood gushing from his arm.
D. Stain is faster than him as well, and Shouto can put up firewalls in time to stop stain from touching him, he can do the same here and unlike Shouto, azula wont resist the fire that Shouto produces.
E. Flashfreeze Heatwave, a move which has shown to OH.KO base Deku even when weakened via being clashed against and blocked by multiple of cementoss’s walls, if that lands (which it will, it’s hundreds of meters), it’s game over, even if not instantly, the damage it causes will be severe enough to be.
F. He can do the thing he did against Iida and Deku respectively, even when he was being kicked/punched, he still managed to land his ice onto them, and he’s not aiming to capture here, he’s willing to kill, so yeah, necrosis ice
Note: Ice Necrosis is what he did against the Nomu. the reason it fell apart completely was because of ice necrosis