On Dreamland it's quite easy, you're having a lot of trouble with the laser spam, it makes you stuck in shield. What you need to do is go single player mode and just learn to slide all over that goddamn stage, utilize platforms. Right now you're only just jumping on them and falling through them, you need to learn how to utilize your wavedash, especially against Falco. When he spams his lasers on the ground, don't even bother staying there. Take it to the top platform and drop on him from above. If you can force him in shield, great, don't even care about shield pressuring, go for a shinegrab as soon as you can.
Falco isn't a fun match-up until you are technically advanced. Falco's tech skill requirment is a lot lower than Fox's to be just as annoying, but once you get there where you can waveland/dash all over the stages and through his lasers, you can beat him. Falco is about getting more technical, getting better movement, being faster. If you're slow, he dictates the game, and screws you over.
Learn to play faster against him.
EDIT: As I keep watching, it looks like you do have the right idea at some times, but at other times you're at a loss for what to do. You're not putting enough pressure on the Falco with movement which lets him dictate your game.
And you throw out unnecessary moves quite a lot. You'll be surprised how great it is to land without doing an aerial, you can instantly run away instead of waiting for the aerial lag to finish. It's a part of keeping your movement.
On Battlefield, you're utilizing the platform better. He spams lasers, you retreat to platforms. Good stuff. Sometimes a shine for a laser from across the stage can do wonders in getting him to stop. You could powershield but shine is the lazy man's way.
Too bad you lost that match, you played well but on the last stock I noticed you got nervous and started playing worse.