yes
They laugh at me when I fall down the stairs.
Conjunction
early
Don't drag my book bag on the floor. Slight atmospheric drag can cause a satellite to slow down and eventually fall back to Earth. Wild horses could not drag me from a good chariot race.
It is correct to say ''He will fall down''
it will slow the fall down a little.
to fall is infinite verb.
PREPOSITION
I sure hope I don't fall down.
no. the sentence should be 'the ball fell down'
Depression
The leaves fall down.
They laugh at me when I fall down the stairs.
Conjunction
The only thing wrong with this sentence is that both parts of the sentence are in present perfect. Rewriting the sentence without contractions: "He has gone down, and he has not put his hands out to break his fall". One wouldn't say this. One would say, "He has gone down, and he did not put his hands out to break his fall"; or "He went down, and he did not put his hands out to break his fall".
She laid the book on the table before leaving the room.
It will fall fast if it is heavy and slow if it is light because the gravitional force is pulling it down to earth