Stars (and essentially planets) won't move relative to each other in one night, they will move collectively across the sky because of the Earth's rotation. (Planets will technically move amongst the background stars, but you would not notice their relative movement unless you observed on a night to night, or week to week basis, you will not notice thier relative motions to the "fixed" stars with the naked eye in one observing session).
They also both are capable of twinkling, I have seen planets twinkle when they are very close to the horizon, but for the most part, you will only see the stars twinkle. (For a deeper explaination, look up the term "scintillation").
Satellites move steadily across the sky. You will only usually see them the first couple of hours after sunset or the last couple of hours before sunrise. If you think you see one at "midnight" you are either at a very high latitude during your hemisphere's summer, or you are mistaken. Satellites (unless they are "tumbling" rocket payloads or irridium flares) will have a consistent brightness until they fade out (usually because the angle of sunlight reflection gets poor for the observer, or they enter the earth's shadow). They will not change direction or speed, but sometimes you could be decieved into thinking the latter happens because of the 3-D angle you are looking at it. A satellite is usually only visible for about 30 seconds - 3 minutes, before it's orbit takes it to a location to where it cannot reflect sunlight to a stationary observer.
Planes will change direction (unless they are WAY up there, and just completely passing your town by). Have blinking lights. If they are low on the horizon, they might appear stationary for a couple of minutes, but will not remain in the same part of the sky for any considerable length of time.