Right! However, the word “superannuation” is used differently in Australia. Australian superannuation funds are more like a KiwiSaver account, and money received from the government is called a “pension” or government benefit.
It’s complicated, and depends on how long you’ve been in Australia, what visa you’re on and a few other things. You may not be eligible for a pension in Australia, depending on your visa/residency status – however, it is highly likely that you would be able to receive something from either the New Zealand or Australian government. Often, it’s the case that, based on how long you were in each country, your pension will be “topped up” by either Australia or New Zealand.
Theoretically, yes. It may not be the “full amount” though, especially if you’re receiving a payment from the Australian government. It also depends on how long you’ve been in/out of New Zealand. Keep in mind, income received from NZ Superannuation is taxed by the Australian government in the same way that income from work is while you’re in Australia.
Unfortunately, we can’t give you specific advice! That’s best left to a financial advisor or other professional, who can take into consideration your particular circumstances, which include your assets (e.g. property) and income. All we can do is give a short outline of a few things you might not know that might come in handy – think of us as food for thought rather than strict guidelines.