Differences between 摔，落 and 掉
摔: stress on the power, usually for human and animal stumbled, or things thrown by people.

落: a process, usually slow 

掉: lost control, stress on the difference from the original position and new position,

So a plane landing successfully could be 落下 from sky, if the plane get some troubles and fall down, that could be 掉下 from sky.

A famous quote 天上掉下个林妹妹 from 红楼梦, 林妹妹 is a girl in case you don't know 红楼梦, she was a immortal live in heaven.

What if 天上落下个林妹妹, then 林妹妹 might use some magic to land on the earth. That is a common scene in a fantasy novel.

What if 天上摔下个林妹妹, a funny scene, imagine she walks on the heaven, then stumbled then hit the ground by head...

But 天上掉下个林妹妹, weird and unbelievable things happened, a beautiful girl fall from heaven and stand just in front of you.