You might try a bit of HUCA with AA, I've heard anecdotal reports of AA doing it even without trans-oceanic segments.

Presumably yes if your first segment is MH then the online tool would ticket it with MH. The only exceptions I've heard for that yet are RJ and AT seem to ticket with QF. But if you see your fare in AUD that's a red flag and I'd not use the online tool in that case because if it's QF they will ticket immediately after putting your payment info in and you're then stuck with them as the owning airline for the long haul (something you don't want). It's different than CX where you enter your payment info into the online tool, but it still just gives you a PNR to call and get a payment link (allowing you to make last minute changes that couldn't be done inside the tool before paying as well).

Someone else will have to chime in about their customer service center, I've never dealt with them that deeply, only airport staff who are perfectly fine in my limited experience.