That matchup is better for Luigi than Fox or Falco I think. It's slightly in Falcon's favor but it's definitely doable, especially if you consider spacies doable. That set was definitely all Mango, not really the matchup.
I mean there's combo **** both ways, though it's not like either has guaranteed death combos on the other, they happen often enough.
As far as approaching goes, Falcon's gonna try and dashdance grab or approach/zone with nair/knee for the most part. Try not to get caught above him and you have good ways to respond to his options.
If he's doing an nair going forward and you expect it, you can usmash/utilt through the nair, CC it at low percents to downsmash, or shieldgrab it probably. If he's just kinda zoning with nair you can try and call it with a wd usmash, or kinda challenge it with bair/chop.
I have more problems with knee as you can't really shieldgrab it and trying to usmash it is riskier, but you can wd back dsmash or something.
Against falcons who run back a lot you can call it with a full-length wavedash and you can often hit them when they dash back, which is something few characters can do as well as Luigi.
As far as combo options they're mostly pretty intuitive I think.
I haven't figured out how to optimally DI against his combos yet. Usually Down+Away is definitely the best option, but against some combo patterns survival DI seems to get you out also.
I think FD is pretty bad for Luigi in this matchup and Yoshi's is really good.