Like so many phrasal verbs, use depends on context. You can 'fall down the stairs' or 'fall off the chair'. Something could 'fall off the table'. You can simply 'fall down' [collapse]. Something standing up can 'fall over', or a person can 'fall over' something in his path e.g. 'he fell over the box'. 'Fall out' also has the meaning 'to no longer be friendly with' e.g. He fell out with his family. As a single word 'fallout' from an event means 'repercussions' or 'consequences' of the event.

We use this expression in the past tense. The boy fell down. The statue fell over due to heavy winds. If you are not careful, you could fall off the cliff. (this is OK in the present tense) The Army platoon was told to "fall out" to be dismissed. Again OK in the present tense.

Fall down - describes a person or object falling to the ground, no specific direction Fall over - something or someone falls sideways. Often interchangeable with fall down. Fall off - A person or object was on something and fell so that it is not on there anymore. This one should include some indication of what the person fell off of. He fell off the chair. The picture fell off of the wall. Fall out - Similar to "fall off" but the item or person was in something and fell in a way that it is no longer in. I fell out of the car when she pulled open the door. The feather fell out of his hat. His tooth fell out [of his mouth].

You can also "fall out" of something, "The skydiver fell out of the airplane"