I'll try my best to read into every situation so you can better understand some of the mistakes you are making. Taking the quick choices you make and magnifying them to reveal their true importance and scope in the context of competitive play, would definitely help you improve. Hopefully you don't take this as me reading too much into the finer details.
0:38: If you're mid combo and your opponent still has a double jump, or you're not sure if you can still combo (you throw out a nair here) - its best to relax and wait for them to do something. Most professional players (Ken comes to mind), are proficient at knowing when not to attack, then waiting for the right time and hitting them when they double jump or try to retaliate. Getting comboed sucks, and you know that once a true combo string has ended your opponent is looking to retaliate. To do something...anything. Since you knocked him off the side of the stage like that, waiting for that DJ and ftilting/fsmashing or even blocking would have spelled his doom. He had no where to go, but you threw the nair out without really understanding the situation. It almost cost you your stock.
While I'm on the topic, Ken is notorious for this kind of thing. Starting a combo, noticing gaps and breaks in strings, and tippering through DJs and aerials. He uses the pressure he created with his opening combo as a guide. Its a great habit to get into.
1:04: You should never miss an edge-guard like that. You had more than enough time to grab the edge and take that stock. Pinpointed dsmashes are okay, but if you miss there is huge lag. The window for punishment is alot bigger if you miss with dsmash than with many of your other edge-guard options, so use it sparingly (If spacies illusion quickly and you aren't positioned properly, etc). Falling off with shine, grabbing the edge, or even SH dair would have been good options in this situation. Falcon's upB can never truly sweetspot. Some part of his hand is always above the edge even if it doesn't look like it. Leave the laggy **** at home and go to work once you knock him off the stage.
-On your second stock, too many random nairs, too many missed usmashes. You looked almost confused in your execution and movement. At 1:29 for example, there was no need to nair right in his face AFTER he had recovered from his knee, because he'd obviously be dashing away. Against good players, any whiffed aerial is open to counter-attack and big damage. If you aren't sure of how to land a hit, then stick to what you know. Dash-dancing is good, FH auto-cancelled and SH bairs are good for spacing and putting up a wall, dash attack is good for overshooting vs. other dash-dancers. Play to Fox's strengths and use your execution to have a planned method of approach and defense, rather than just spamming usmash or running around aimlessly, missing opportunities left and right.
2:00 onward: So focused on landing a shine at this point. I guess your strategy here was "If at first I don't succeed, go for it 5 more times 1!!!11!!". Pace yourself; more thinking and less random button pressing. If you CCed him back with grab or your own jab, it would have left you in a much better position.
3:05: I think you know what happened here...this goes back to the first thing I said at 0:38. Combo ended, the shine -> bair was completely unnecessary - yet you went for it. You had good pressure going, but when the combo ended you just kept going and going. Good Falcons land a knockdown with dair like that, GGs buddy.
3:15: I have no idea how you missed this edge-guard. Why laser, when you could have run across the stage and simply ended the match? The shine spike was a good idea, but it seemed oddly placed. Random lasers for damage when he was already off the stage and at kill percent, then a missed shine. The shine spike was a good plan, but it was poorly executed. The lasers weren't needed in the slightest, and really only made it more difficult for you to catch up with him. If you want to get better and have a cleaner more professional looking Fox, you're going to have to get right to the point and get the job done.
Hope I didn't sound too mean! I watched your videos waay back when, and it seems like you've improved alot since then. Mostly, I just notice more technical consistency. You're mind work needs a boost if you want to improve your Fox. Hope I hepled.
I'll be sure to give some light commentary on match 2 as well.