Continue. How do you suggest we get back? What are some good ways to take advantage of the opponent being at the edge?
For getting back on stage:
-Waveshield from the edge -> roll tends to be pretty good. A lot of people will throw out one attack that hits the shield and then do something else that the roll will get around. You might still get hit, but chances are you'll get to the other side of the opponent and at least get away from the edge. The opponent can knock you back to the edge in a variety of ways, but that doesn't happen often, which I think has to do with the position people like to occupy while keeping somebody at the edge. If the opponent isn't in a good position to throw out an attack when you choose to waveland onto the stage, waveland -> something like ftilt/utilt can work.
-Wait on the ledge a bit. Lots of ICs players (myself included) like wavelanding onto the stage as soon as they can, so some people will preemptively throw out an attack or start charging a smash in anticipation of this. If you notice your opponent likes to do this, you can often just wait and then either ledgehop -> fair or waveland on stage into an attack or roll depending on the circumstances.
-Ledgehop -> fair is on the janky side of recovery options from the edge, but it does tend to beat a lot of moves that aren't disjointed if spaced well, so you can sometimes use it against somebody who is throwing out moves when you're on the edge. It's kind of worthless against characters like Marth and Sheik, though.
-Something that I rarely do even though it probably is really good is ledgehop -> stationary waveland right at the edge of the stage. Like the usual waveland onto the stage, it gets you off the edge quickly, but it doesn't force you to slide into your opponent. Since people usually position themselves kind of far from the edge when trying to keep ICs from getting back on in anticipation of the long waveland from the edge, this can be pretty decent against most characters who aren't Marth. In this situation, characters that don't have big, disjointed hitboxes may whiff an attack, which you may be able to punish with something like ftilt or fsmash.
-Also on the jankier side of things is ledehop -> diminished ice block. This is inherently situational since you need to have shot an ice block while off-stage in order to have the diminished ice block. Like ledgehop -> fair, the opponent can easily hit you out of your double jump in anticipation of this, but this works in a few situations that ledgehop -> fair doesn't and it's probably not something that anybody is going anticipate unless you've already done it a few times. It's nice in that it can work against a lot of characters. For example, it's one of the only things aside from the waveshield from the edge that can actually help you get around Marth. You can sometimes combo off of the ice block, but at least for me, it's hard to judge when you can legitimately follow it up with a grab or ftilt.
-Once you're actually on the stage, if there's a platform overhead, jumping onto to it, wavelanding towards the center, and fastfalling off the inner side of the platform and using bair to cover yourself can be good. Even though ICs fall slowly, this still tends to be pretty safe as long as you can get to the other side of the opponent since fastfall -> bair can be hard to punish. If you don't think the fastfall -> bair will work on your opponent for whatever reason, instead of trying to fall from the side of the platform to the main stage, you could double jump and waveland onto the top platform. This generally is harder to punish than fastfall -> bair, but how good it is to be on the top platform varies hugely by stage and match-up, whereas fastfall -> bair always puts you near the center and can put your opponent in a bad position.
There's probably more I'm forgetting, but I think that's a decent summary of returning from the edge with ICs.
I don't have as much to say about ways to take advantage of the opponent being at the edge. It tends to be a strong position since if you ever think it's not worth challenging your opponent at any given time, you can safely retreat while still maintaining a better position than your opponent. It also tends to be good since your opponent doesn't have much space to retreat to, so his options are more limited than they typically are otherwise. Also, it's not usually a big deal if you get hit by your opponent since you don't have much to lose if you get towards the opposite side of the stage, whereas your opponent has a lot to lose if he gets hit off-stage. There are characters that can knock you off-stage from this position, but it's usually not a big deal since ICs are quite gimp-resistant. Be very cautious about moves like Peach and Samus' dsmash, though, as they can knock you pretty far off-stage and can lead to early Nana deaths and legitimately bad positions.