I can answer your first question quite thoroughly, so I'll.. just answer that one, lol.
The C-Stick functions in different ways depending on what setting it is in. There are two different ways to direct the Control Stick, of course. You can Tilt the Control Stick, or you can Smash it. The C-Stick set to Smashes and Specials will automatically interpret every input, regardless of how hard the C-Stick is pressed, as the equivalent of Smashing the Control Stick and pressing the associated button. The C-Stick is not analog, and so it cannot differentiate on its own between Smashes and Tilts.
As you may know, however, it is possible to perform Tilts using the C-Stick by pressing both sticks in the same direction. If you Tilt the Control Stick in a direction, and press the C-Stick in the same direction, the move is registered the equivalent of Tilting the Control Stick and pressing the associated direction. For C-Stick Attack setting, every C-Stick input is regarded the equivalent of a Tilt plus the associated button, and there is no way to achieve Smashing the Control Stick plus the associated button.
So, what this means is that if you are at or past the peak of your jump and you simply press the C-Stick in a downward direction, it will automatically fast fall, regardless of how hard the C-Stick is pressed, because the game interprets this as if you had Smashed down on the Control Stick, which would clearly fast fall. If, however, you Tilt the Control Stick downwards and then press the C-Stick down, you can force the C-Stick to be interpreted as a tilt, the same way you can on the ground, and a Tilted Dair won't fastfall.
So, in summary, the only way to do so with the C-Stick set to Smashes is to tilt the Control Stick down at the same time as you input the Dair with the C-Stick. Additionally, if you sacrificed C-Stick Smashes for C-Stick Tilts (the Attack setup), every Dair you input with the C-Stick alone will not fast fall.
Hope that helped.
