And if whatever sheared off the part of the spaceship/satellite changed it's momentum. If I'm on a space station, and fling something directly towards the earth, from my perspective it will fall directly towards earth for quite some time (probably out of eyesight) before the orbital movements make it behave in odd (compared to on-the-surface) ways.
Uhm no. While you are in orbit you simply revolve around a parent object (a planet for example) but you still are subjected to its (and by proxy it to yours) gravitational pull. Eventually something that came lose will deorbit.
Keyword here is eventually. Sure it will, but what it definitely will not do is accelerate towards planet earth at what looks like 9.81m/s². AKA falling.