On the first question, the clear answer for those who have been watching the development of Chinese naval power is a firm “no”. The PLA Navy is now the largest in the world by ship count and is well-equipped with advanced blue-water warships, plus the auxiliary ships needed to keep them at sea far from home. It has maintained naval task forces on a continuous basis outside the Pacific for fifteen years, and has sporadically deployed task forces far from home to places like the Baltic Sea and Alaskan waters. China is now, by far, the world’s dominant maritime power by every measure other than sheer naval tonnage (US Navy ships are, on average, still larger), and its maritime interests are global in nature. That we also see global Chinese naval power should come as no surprise.
Next, what was the nature of the challenge that China posed with its operations in the Tasman Sea? What it was not was a legal challenge. Under international law, the Chinese naval task force was fully entitled to conduct military operations — including live-fire exercises — on the high seas between Australia and New Zealand, no matter how uncomfortable it might make both countries feel. Such a right for state vessels to operate freely also exists within nations’ exclusive economic zones (EEZs), though some seem confused on this point — including China, which regularly interferes with foreign air and naval operations within its EEZ.
To be clear, though, what China conducted was not a freedom of navigation operation (FONOP). When the US Navy conducts a FONOP, it does so for a specific reason: to challenge excessive maritime claims made by other nations that are inconsistent with the international law of the sea. And it does so not just with respect to its adversaries, but sometimes even to its allies and partners, such as FONOPS conducted in recent years challenging claims made by Taiwan and Japan. In China’s case, there was no such maritime claim to challenge, as neither Australia nor New Zealand make improper claims to the Tasman Sea. As such, this was not a demonstration of Chinese freedom of navigation. It was a show of force.
Regardless of the legality of China’s naval operations, however, they were conducted in poor form for a nation that claims to be a responsible stakeholder (though it can be somewhat choosy in deciding when to act as one). To avoid risks to civilian air and maritime traffic, the norm is for such exercises to be announced well ahead of time, not over the radio to passing aircraft that may or may not happen to hear warnings in situ.