I'm gonna try to do a quick analysis/things to pay attention to in the first match.
1) I dunno about P:M but as far as Melee goes, Jump canceled grabs are crucial. Immediately on the start you missed a JC grab, which if you don't know how to do that, is jump and grab at the same time. [y+z, x+z]
So be sure to work on that if it's even in P:M. You'll know the difference because you'll do the standing grab animation instead of the running grab animation.
2) MOVE. You're a Falcon player, if you're not dash dancing around, you're attacking/defending/getting ***** offstage. Those are your 4 options. DD always, it allows you to really threaten space and to be mobile. It's easier to move if you're already moving. So at 0:10, you just took that utilt from Fox and you could've ran away, came back after the utilt, and grab->****. Also, after that you rolled away and literally stood there. Just stood there. If you leave Falcon alone for a few seconds, he's always moving and flexing, which is important because he's a character who always movesssssssssssssssssssssssssss. So moveeeeeeeeeeeeeeeeeeeeeeee
3) Tech chases are important, I dunno how long you've been playing but I'm gonna assume you're a newer player with fewer tournament experience outside of your normal area. 0:19, he literally rolled right up to you and you ran away to tech chase over there. You'll pick this up as you keep playing, but try to really start to learn the roll distances and the mindgames of the players. Does he always roll inwards? Punish him with a stomp/raptor boost/another grab. [you did this at 0:36 if you want an example of what I'm talking about] Also, if they're near an edge, they almost always roll in if they're a newer player, so keep that in mind. This goes with number 2. Stomp, grab, rb, do SOMETHING, just move!
4) Ledgeguard. Now I've played the Alpha of P:M, and I know that people fall like a ROCK in that version of the game, so I'm not gonna be too hard on you for that double knee about 2 miles below Fox. I know what you were trying to do and that's okay, but a better, safer option is run out with knee, if it hits with the weakknee/doesn't hit, jump backwards WHILE doing a uair [inputs being jumping with controlstick, pressing a, and holding away is the easiest way to do it]. You still wouldn't have hit him because of how high he was, but in general this is a good idea. If I find a video I'll show you. But anyway, Ledgeguarding is one of the MOST IMPORTANT things about this game. That, more than anything, is what sets it apart from Brawl. Yes, 0-death combos are great [and I feel that that's what you're trying to do a lot here] but 90% of people die from edgeguards, not from being knocked off the sides at 130% from a knee after a 0-death. Like I said 0-deaths are fine and great if you can do them, by all means go for it! But remember that a gimp is always safer and more consistent than a nair->nair->uair->uair->uair->knee on Marth.
Also, as portrayed at 1:44, watch the recovery. If you miss that opportunity to hit, you've let him back on stage, and that's bad.
5) Recovering. This actually gets a lot harder than it is now, so learn well young padawan so that you may **** with falcon later! People will really start to give Falcon's recovery a hard time. So learn to 1) be smarter with your recovery, which I'll cover later, and 2) remember all of your options available to you. You can Falcon kick, which gives you your double jump back. You can double back to the ledge with your Upb [move forward, then move backwards] and most importantly here, you can ledge tech. When you are below the stage and recovering, always press R. you have 20 frames before the attack hits you, and you can tech it. Smash DIing helps too, but I don't wanna get into that. If you had pressed R while recovering at 1:10, you would have teched that downsmash and lived. So remember those kinds of things.'
6) Consistency. 3:10, you kneed and broke his Firefox. While technically this can go under 2, I did this to show you something. If you had consistently kneed, or done my favorite edgeguarding move, the Lazy Falcon [utilt], you would have absolutely WRECKED him for going offstage. The way you want to play against other players, is that if they're offstage, they are DEAD. They're not going to show you any more mercy, so absolutely WRECK them offstage. But anyway, the point is that you changed your tactics. You went for a stomp [which I'll let you know, you have to hit with the extended feet, not your chest] instead, and you missed the chance for a 14% gimp because of it. Be consistent with your options, as you usually pick them because they're the best option. While you should always vary your responses, you should never change from a response that works to one that doesn't, is what I'm saying. Make sense?
7) Random things. 3:17, you can grab a fox out of Illusion. Do that. Also, you're playing a very common match up: Fox vs Falcon, and Mindgames vs Tech skill. Fox vs Falcon is summed up like this [in a nutshell]: DD, grab, do something, repeat. The something depends on what the occasion calls for, such as a knee on the ground because they missed that tech after the dthrow, or a stomp tech chase, or another grab->dthrow off edge->dropzone [look it up, SS dropzone] But you HAVE TO GRAB THEM to death. Fox vs Falcon is bad punch for punch, because Falcon simply does not have the priority to deal with that. So you have to GRAB. So remember that, it's one of the best pieces of advice I've ever gotten.
Secondly, you're fighting mindgames vs tech skill. This fox is fairly technical, especially for P:M [I played around with it and couldn't even WD out of shine, though I can in melee] but the problem is he's not very smart as far as showing off. Dark is the same way [watch Dark vs Ghost, they're great players]. But so you have to capitalize on this. An example is the consistency section I described above. If he messed up a technical thing, you need to PUNISH HIM hardcore for that. He's just kinda running around, doing a lot of tech things because he can [SHDL, playing around on the edge with FF stalls, shine->bair when there was no one around at that point]. So you need to wreck him when he does this. Tech doesn't matter when it doesn't hit.
Also, don't ever ever ever ever ever Falcon Kick. ever. For any reason. Except that you're recovery, or that you're Darkrain. But you're not Darkrain, so don't do it unless you need to recover.
I hope this helped, and that you didn't take offense, it's just the way I write. I may do one for your second video, but not now.