Is a satellite orbit around the Earth Lyapunov stable?

Presume there is a satellite orbiting the Earth in an orbit that follows a closed path around the planet (that is, escape orbits are not permitted here). As I understand it, there are two possibilities, ignoring the massive timescales that this might require:

1. The orbit can decay due to the action of the atmosphere
2. The orbit can expand until the satellite eventually leaves orbit. As I understand it this happens with larger bodies, like moons, around planets, but not satellites. I also could be wrong here.

Considering the $langle x, y, z rangle$ coordinates of the spacecraft in a suitable coordinate frame and their associated derivatives, in case 1 above the orbit would be stable in the sense that it decays to the origin of the state space, if the Earth were a point mass centered at the origin. However, it isn’t. Would such an orbital decay still be Lyapunov stable?

Is case 2 possible? In case 2 the orbit would be unstable in the sense of Lyapunov and just about everything else, correct?

Is there a 3rd case in which the orbits are actually stable in the sense that the coordinates in the state space are bounded and never zero?