The normal process is that you always have at least one US and one Russian Vehicle docked to the ISS. In emergencies, each crewmember uses their spacecraft to return to earth.
The normal rotation is that an additional spacecraft arrives at the ISS (so there are now 3 vehicles docked in total) and then the older spacecraft leaves with its crew. So before the single dragon leaves, a new dragon would arrive.
I think the general idea is to always have at least some Russians and Americans on the ISS at all times (although they are doing swapped missions now so even having only one vehicle left would ensure that most of the time) and to always have crew on the ISS, even if one vehicle needs to return early due to technical problems.
The Crew-10 was not a rescue mission because they just rotated with Crew-9 which carried the Starliner Astronauts back. Crew-9 could be called a rescue mission because they took back the Starliner Astronauts. But Rescue makes it sound more urgent and dedicated than it actually is. They would have flown anyways, just with more crew.
That is exactly what it is. That mission has been scheduled for more than 6 months (though the exact date changed a couple of times for technical reasons).
I think the general idea is to always have at least some Russians and Americans on the ISS at all times (although they are doing swapped missions now so even having only one vehicle left would ensure that most of the time) and to always have crew on the ISS, even if one vehicle needs to return early due to technical problems.