These are low-orbit satellites and they will eventually "fly over" every point on the Earth up to their maximum inclination. Only geo-stationary satellites are "hanging above an area" and suffer from high latency because of the speed of light.
Legally speaking "airspace" does not extend beyond the atmosphere. There are treaties for this, otherwise almost all satellites would need approvals from almost all governments.
However it is supposed to work and however it does work at sea, is the situation similar for space?
> What if countries decide to extend the airspace to the aerospace?
I imagine the US would consider it an attack and retaliate (maybe economically, militarily, or covertly) against the "attacking" country.
You can find out more here: https://en.wikipedia.org/wiki/Space_law
This is basically unthinkable.
Attempting to knock down all the satellites that ever fly above your country would mean knocking down every non-geostationary satellite that ever reaches your latitude (or any latitude farther from the equator than you).
Satellites are a key part of how we all know if anyone else is launching nuclear bombs or doing anything else so stupid. In the event that a country tried this I would expect that the foreign reaction would be very extreme. In the event that a country succeeded I would put the odds of nuclear war at above 50% and of conventional war at near 100%.
On the flipside you might almost get away with knocking down a few satellites with relatively minor reactions (at least compared to war, and if you had some good justification), as long as you don't try and knock them all out...
Of course, this logic doesn't apply to suborbital flights. Any country with the means will probably just shoot down unauthorized objects on suborbital trajectory into their airspace.