For timeing:
You can't air dodge until you're in the air, and your character doesn't instantly jump. The game runs at 60 frames a second.
Jumpsquat duration varies by character. For Captain Falcon, it's 4 frames. You can find other jump squat lengths here:
http://smashboards.com/threads/p-m-3-0-statistics-list-shff-speed-weight-falling-speed-etc.335019/
On frame 5 you are in the air and may air dodge.
When you land during air dodge there are 10 frames of air dodge landing lag. You can't do any actions during this time. For some characters they can still be moving when this endlag ends, and for others they stop sliding before their endlag ends (of course this also depends on how far you intended your wavedash to go as well).
Note that if you slide off a ledge, you will cancel the air dodge landing lag. This can be done with aerials as well, and is edgecanceling. As a result, wavelanding on a platform and off the ledge to attack is a common use of wavelanding.
For use:
Wavedashing opens up options when you're coming out of a run or dash. If you have a good reason to use tilts (which is probs never or rare in neutral for C. Falcon), then you could wavedash to do just that. Wavedash is typically used to go away from the opponent simply because of the landing lag from it, but you can certainly still use it as an approach depending on your character. Also, it's probably the best way to get out of you shield if the opponent isn't right next to you. Wavedash out of run to retreat is a good way to make it look like you committed to an attack and then be able to punish if they take the bait.
To clarify, "neutral" is when both players are on the stage and not near a ledge. It represents both people being in a relatively good/neutral stage positions. You can also use wavedash to help combo or juggle with tilts, though I'd imagine C. Falcon would have better options in most cases.
Wavelanding has lots of uses. You can hit someone up, waveland on a platform and grab them or tech chase them. You waveland on a platform (on the way up, so you don't have to wait to fall back down on it), so that you can get higher before jumping to juggle someone. You can use it on the way down on a platform and edgecancel to either get some surprise range and attack someone below or to increase the distance between you and your opponent (if you feel you are too close for comfort). I sometimes short hop fast fall with no aerial to see if I get a reaction. If they shield I run up and grab (nothing to L cancel so this can be fast), and if they don't shield I sometimes go for a surprise waveland towards them to see if that gets them to retreat or approach. Dash away after wavelanding towards them and if they take the bait and miss, you get a punish, and if they retreat you just stole some space. The closer they are to the ledge, the worse off they are.
