Yes, sort of, but that’s mainly useful for torque rather than thrust as thrust relies on (if I’m getting this right) field gradients rather than absolute field strength. It’s not nothing, but it might as well be.

I back-of-enveloped a launch system with a very big magnet on the ground, supplying a much steeper gradient to push against, and it was still crazy expensive.

(I wonder if it would be useful for skyhooks?)

this is suggested frequently in these threads. it is already used in the very limited application where it is useful.

https://en.wikipedia.org/wiki/Magnetorquer

"It is also impossible to control attitude in all three axes even if the full three coils are used, because the torque can be generated only perpendicular to the Earth's magnetic field vector."

the non-earth orbiting mission i worked on didn't have any; it used little thrusters to desaturate its reaction wheels.

Yes there are various forms of electromagnetic drives that use the earths magnetic field for small tasks like rotation and (maybe) station keeping. There are a few types, some which use propellant, and some that do not. More info here: https://en.m.wikipedia.org/wiki/Electrically_powered_spacecr...

Yes, I remember reading about people using this to deorbit satellites... though I can't find the link right now.

Yes, satellites already do this.