Follow the money...
I think there's more to this than simply an abusive stepmother who killed Z in a rage, buried her in the garden and didn't report it for a couple of days. If that were the case, I think AB would have given her up already.
Regarding how Z was allowed to move here from Oz, having gone through US Immigration Services myself, I would say EB and AB married because they had no choice if they wanted to move Z to the US. The application for permanent residency is made by the US citizen, not the person immigrating. EB could apply to bring AB into the country as a fiance, but unless they are married, there's no relationship between Z and EB, so AB couldn't get her in. It takes a long time to get the permanent residency, even for a spouse. I don't know about NC, I'm in a different state, but I'm guessing maybe 2 years. They almost certainly arrived on the visa waiver program, which as has been said, is a tourist, non-working visa, with a maximum of 6 months, although more likely they came in on a month visa only (see below). Once in the US, EB could then apply for a change of status and start the long haul to getting a green card. AB would be totally dependent on EB during that process, although after a time a spouse can divorce and still have rights to stay in their own right. I'm not sure how long that is, or if AB would even know about it. Also, the whole process is quite expensive, with filing fees and so on, maybe around $1,500 for the two of them.
A December arrival fits with Z ending her Australian school year before the move. The main school vacation in Australia is January, being high summer and equivalent of our August, so the new school year starts after that. It also wouldn't raise any flags at the US border, since many families move around at Christmas time internationally. However, US Immigration knows a child needs to be in school, and one of their jobs is to make sure children do not illegally register in public (Australian translation=state) schools at taxpayer expense, hence they could only get Z through on a tourist visa of a few weeks, without raising flags.
As for AB's status, it's possible he is working off the books, because he may not even have work authorization yet, not sure if that's known or not. It would depend at what stage in the process they might be, or even if they started it, but almost certainly it would have been a cause of friction between them. The whole system is designed to be as difficult as possible to get through (same as most countries I might add, so I am not having a go at US particularly, it's just the way it is). If EB was involved in anything illegal, even if AB was clean, that could be a HUGE problem. If you're writing bad checks, or involved in drugs, you're not getting a green card, and even if you already have one, you can be deported. Even a misdemeanor is a problem, so he's almost certainly not going to be allowed to stay if he's found guilty of any of these current charges, aside from the bigger question of what happened to Zhara.
I can't help feeling what a dreadful shame AB didn't stay in QLD, it's so beautiful there, I know the area. Like everyone else, I'm praying that Z's found soon and that all the unanswered questions are answered so the family can find peace.
In my heart, I'm hoping it was something as simple as an accidental drug overdose - that she experimented with someone else's drugs and died instantly by accident - and that now they're just being silly trying to cover it up. That's because I can't bear to think of that beautiful child being treated cruelly and such a bright star being extinguished so young. Bless her.
My 2 cents.