Yeah agreed! I think that since Azula didn't treat either of them well pushed them toward each other, though we never really saw that until the Boiling Rock episode.
It would be! I bet they had some cute normal friendship moments. Ty Lee probably would have been there for Mai when Zuko left but I can't imagine Azula would have been sympathetic.
Ugh yeah Azula would totally be the type to just make it worse. I could so see her making little comments like "I wonder what Zuko's doing now" just to make it worse.