I could be mistaken here but it's my understanding that when the Royal Family is on official business to a commonwealth country they don't fly commercial. Instead, there is a dedicated plane for them. Now on the ground I'm less certain about whether they are chauffeured in their own (UK government) vehicles or those of the host nation. When POTUS visits other countries the secret service always brings over their own vehicles and equipment for security purposes.
What I will say as a Canadian hearing the news of Prince King Charles visiting the country is I think it is a good thing. Australia, like Canada has a rich tradition of the Monarchy. Maybe it is passé, and Australia needs another referendum on becoming a Republic, but for the time being this is the system we've got. And look, I can understand the animosity by some towards the monarch, the interference with government. This is something frankly we haven't had to deal with. However, with that being said, one must appreciate the history, the tradition, the continuity which is why this form of governance (love it or hate it) has withstood the test of time. King Charles visiting this country is maintaining that obligation to the monarchy, to the commonwealth and traditions and is vital given the passing of QEII. For most Australians (and most Canucks, Kiwis, etc.) Elizabeth was all we knew. Until quite recently, I kept referring to Charles as Prince since for decades that was his title. The other point that is brought up here is these are challenging times for Charles. He's facing cancer and other issues and yet he kept pressing on. As you can imagine being of that age with these medical conditions and travelling such great distances does take a toll on one's body regardless of how plush the seating may be.
That's my toonie on the current events.
-RooFlyer88