Foreign countries buy USD through trade. Japan needs dollars for international trade so the US Treasury prints dollars and gives them to Japan and in return Japan gives the US Nintendo Switches or whatever. Those dollars go into the international trade system and some of those dollars will just circulate internationally indefinitely and won't ever make their way back to the US, hence the perpetual trade deficit. This is a great deal for the US because at the national level they effectively got those Nintendo Switches for free.
It’s not for free. It’s in return for being under the US security umbrella, which costs the US about $800 billion a year
Of course that umbrella could soon be gone, so it would be a moot point
That’s not how that works. If Japan needs USD it goes to the forex market. That market represents a massive trade flow.
It doesn’t matter which currency you pick in that world apart from capital control. As long as it’s reasonably stable you flow through it with many billions of dollars a day with ease. The conversions are effectively free because the spreads are tiny.
Using the US dollar to trade between two countries that are not to US does nothing to the the currency. It just shifts a deficit.