So about a day ago, I decided to do some Anther's laddering. I had about 3 matches I remembered to save replays of, so here they are for your amusement and critique.
So, 2 things:
1. Critique me.
2. (For anyone who plays as/fights against Captain Falcon a lot) Should Falcon have used Falcon Kick more often? (Because a friend of mine thinks he should, but I feel otherwise, as I was keeping myself relatively safe and any moment where he could have Falcon Kicked would have been better served by Dash Attack or Dash Grab)
I only watched your fight against MrWho. You fought well in what I think is an annoying match up, but I feel that your ledge game can use some work. When you have your opponent at the ledge, you seem to really like the option of a run-back pivot ftilt. It does feel really good when it works but it only covers for a roll. While it's a safe option, it also allows your opponent to do whatever he wants as long as he waits for you to do it, which is exactly what he was doing. He was constantly waiting for you to do something and he reacted to it.
You also seem to like waiting, then walking up to dtilt. I know you're waiting for the invincibility to wear off, and walking forward alone forces your opponent to react, but I didn't really you take advantage of that, and, iirc, you were not being rewarded for it. As a matter of fact, you were being punished.
I'm kind of imposing my own style now, but what I like to do is play Ike's edge game like Marth. I like to be right outside your opponent's get-up attack option and around where they would end up if they decided to roll. You are in a position where they cannot hit you and take away your momentum, so they are forced to do something that is purely defensive. Now you can just react to what they do. Ftilt their get-up attack. Grab or utilt if they roll (turn around if they're behind you). Catch them if they jump. Get them back to the ledge and reset the situation for more potential damage. Go aggressive for a kill once they're used to this. I don't think Luigi can do anything threatening to you form this position besides something like a fireball.
So basically, I liked the options you were utilizing, but I didn't like the timing.
Everything else you did, I liked. I didn't see anything I would have changed, except for maybe delaying the timing of your jab combo when they block it, or just stopping it and going for a grab once they start expecting you to finish it.
Very sorry for the long post. I don't know how to give meaningful advice in fewer words.