What are some English-speaking nicknames for nations like Australia is the Outback? Unoffensive please!?

Unoffensive? GB Shaw: " It is impossible for an Englishman to open his mouth without making some other Englishman hate or despise him. "

Outback is only the less-inhabited part of Australia. Down-under could be used for both Australia and NZ. "The antipodes" is more elegant. Don't confuse "down under" with "down there."

Brits sometimes call the USA "the states." The less-populated part is sometimes called "Fly over country," Of course that offends the few people living in the plains

I've heard the UK, particularly England, called "Blighty."

As the process of seeking more independence for Scotland and Wales continues, I heard a proposal to change the name of the UK to DQ (Dairy Queen objected).

It stands for "Devolving Queendom."

Someone will object to all these, but there are much more objectionable phrases... for instance **** and ******. Not to mention *********.

The United States: 'Murica

Canada: The Great White North

Russia: Mother Russia, The Motherland, Soviet Russia

I couldn't understand your question very well (and I tried parsing it different ways). But it seems you answered your own question: the middle of Australia is called the Outback.

In the US, it would be the Midwest or the Prairies, and England doesn't really have a relatively unpopulated area.