Hey PB&J just watched those matches and a couple of basic things I'd point out:
Gotta have some "set combos" in mind that are kinda your goal, and you can improv if need be. Like against fox on FD Dair -> shine -> dair-> shine -> nair/fair -> fsmash. Of course DI varies, and that doesn't even work if they DI the nair/fair correctly, but that's when you start changing it up by ending in dair -> down smash instead.
Watch vids for sure. That's the best way to kinda have those set combos in your head. Sure, people get creative, they're not all the same, but it's funny how much of it actually IS just the same concepts over and over just applied a bit differently.
Dair-> reverse uptilt is like, the most amazing thing with falco. Against fox it'll lead to fsmashes, on characters like marth it can lead to a quick shine -> bair, or on platform stages against most character you can just do it repeatdly. All the good falcos just do dair -> uptilt repeatedly on platform stages until they see a good chance for a finisher. Also, it's amazingly helpful against jiggs: dair ->uptilt ->shine -> bair... not hard at all, but gets you a good ~40%, two of those and she's already in kill range.
Getting away from comboing, you're doing something a lot of people do which gets them killed against better players... relying on just coming in from above with a dair. In a lot of the matches against fox on FD you'd just full jump/double jump really high above red mist and just come down with a dair. If you want your falco to get as good as your fox... most high level opponents just DD out the way and grab falco before he can shine. It feels like such a good approach (I think everyone starting out with falco uses it) but you have to get rid of it and focus more on getting your hits in other ways.
Besides the fact that lasers are a must, have you tried doing a jump + quick double jump and then shooting one high laser and one low? I saw you full hop lasering a bit, and if you want to cover high approaches without leaving yourself too vulnerable, that's the way to do it. It's really good beacuse you can base the lasers off reaction: after doing a quick double jump and you shoot the high one, if they've run below you can fastfall and shoot a low one, but if they continued their aerial approach you can actually shoot two high ones to stop them.
Last thing: falco's bair. It's amazing. Mango's falco is the best example of using a combination of autocanceled bairs and shffl'd bairs combined with uptilts, shines, and fsmashes to outspace his opponent. A lot of falcos never use this, and I have no idea why. Falco's bair autocancels from a shorthop, allowing you to catch your opponent when they think you're vulnerable. Also, doing this against shields then DI'ing away gets a lot of players to instinctively shield grab and eat an fsmash to the face.
One last thing: you're dairing from too far away against his shield. It's causing low shield stun on the dair, and causing you to hit the shield too high. Nair shine is actually a really good way to prevent shield grabbing, but dair's good to, you just have to watch that. To get around shields, you can also try aerialing and letting your momentum carry you behind the shield.
Those are pretty much all the glaring things I saw; since you're just picking up falco, nitpicking details won't do anything, but definitely look into those. You have a hella technical fox, picking up on falco tech skill shouldn't be much different xDD (If you're real good, add shine JC grab to your play just to mess with people who expect pillaring)
