Angular momentum of different bodies

When the dancer tugs her arms in, the force she exerts points towards her body. If you consider the angular momentum with her body as the origin, that force provides no torque and her angular momentum does not change.

The force that slows down the satellite is probably not a central force. It has a component that is perpendicular to the its radius. That means that it does exert a torque on the satellite, causing the angular momentum of the system to change.

The angular momentum of a satellite in orbit remains the same (actually of planet and satellite) if we can ignore external forces. A satellite in an elliptical orbit will be slower when further away from the planet because the angular momentum is constant.

For a near Earth satellite we need to consider both earth and the satellite. It loses energy to friction with the atmosphere, and as a result its angular momentum is transferred to the atmosphere, but the total (satellite + Earth) remains constant.

The Moon is slowly moving further from the Earth and the Earth's rotation is becoming slower very gradually as a result of angular momentum transfer and energy transfer caused by the tides.