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I wonder how long they'll stay up for. With the lower orbit, I suspect they'll have a short lifespan (unless they have a motor onboard to push them along).
They do have onboard propulsion.
With limited fuel.

Electric flywheels can only alter the attitude (orientation) of spacecraft, not its orbit. For that you need fuel.

Yes but they're argon based ion thrusters which can last a long long time.
Using a pretty simple atmospheric model going from the original 1,325 km to the newest 540 km altitude, the air density doubles (1.990x).

Then there's the increase in velocity since the orbit is now smaller, which is about 300 m/s.

So overall the drag force doubles, but there's no way to tell how long the lifespan is without knowing a coefficient of drag and using a much more complicated atmospheric model that takes into account things like Sun and geomagnetic activity.

These satellites won’t only fly over the USA. How does this work, internationally?

Will they need permission from other countries, who might be wary of these being used for spionage, for example?

Not sure which country you're from, but it's very possible that your country is a signatory of the Outer Space Treaty [0] that defines basic framework for space activities.

Basically it says every country is free to conduct peaceful activities in space, at the same time is responsible for any damage that its space objects may cause. For example the US is liable if a Starlink satellite fails and its debris fall to the ground in your country.

As for espionage, every country conduct espionage. It's very likely that your country's intelligence service either has spy satellites or buys satellite images for surveillance purpose.

[0] - https://en.wikipedia.org/wiki/Outer_Space_Treaty

Yes, but if you want to secretly move stuff around, you want to do the move when there’s nobody watching overhead. If there are 30,000 satellites in orbit (as SpaceX’ claims to want to do), that gets more challenging.