How do I make my character stay down after run_fall? (limelight) :)

You could change it to:
@CHARACTER stands screen left AND CHARACTER faces right AND CHARACTER is run_fall
and that will allow the character to stay down at the expense of not “walking” prior to falling.

or:
@CHARACTER enters screen left and CHARACTER does it while run_athletic_neutral_loop THEN CHARACTER starts run_fall
^which I recommend.

Side note: AND/and THEN/then do exactly the same thing, so whether you capitalize them or not - does not impact your script. (: