EDIT: Juuust kidding, I'm watching the 2nd video at the moment. What I can see right off the bat is that you just run into him without a real plan. The Falco is retreating and you're dash attacking.
Dash attack is an okay attack... If your opponent is on the ground or teching while you do it, but when he's just standing there, shielding to punish you... Also, you did it at low %. Even if dash attack hits at that %, you're gonna get shined for it!
Then you die, too bad, once you get shined there's nothing you can do but DI a lot.
After you die you capitalize on a missed wavedash which leads into a grab. Great! But you ruined the grab. Why usmash immedeatly after the throw? You could have gone for at least u-tilt > u-air or grabs. Usmash just blueballed it :\.
You should be constantly moving, even if you're not near Falco, even if he's not shooting lasers. Just standing with your back facing towards him isn't going to lure him into coming closer either.
That shine out of shield you did there was really good.
Nice finish on his first stock, that's the sort of grabs you want.
Right after he comes back, you got lured into using your second jab. You were hesitant about which side you were going to. You could've gone jump on the platform or hang on the ledge. Your best bet was going towards the ledge because he had below you and the platform covered. You could've also dropped through the platform and B-air him, but maybe he'd not have continued up-airing if you went somewhere else. Ah well.
Now just before you got killed, he was charging the usmash, and you got greedy. You wanted to land and go for a grab, but he let go. You should've dropped a N-air on him. An even better option would be wavedashing onto the stage from the ledge, but I can never pull it off perfectly so I don't blame you lol.
Then at 2:10... WHY DID YOU LET HIM RECOVER. You could've just walked off and drop a B-air and stage spike him (or he would tech but it'd be good regardless), without dying. Never let Falco recover if there is any chance of killing him off-stage.
When you lost your last stock and took his stock: Well played, you should be doing that more.
Just before you got killed and started doing a Firefox. You chose a horrible place to do it. Going straight wouldn't have gotten you the ledge and a bit above it got you spiked. You could've tried going 45 up, but yea.
Basically, here's my advice, judging on this match;
Keep moving against Falco, that went alright for the most part.
Get your tech skill right so you can do what you want. I think there's a couple of times where you know what you want to do but you didn't execute it right. Make sure that goes flawlessly.
Make the right choices, like not up-smashing when you grab at 5%.