Ref Code: ihatefalconandsheik
Y'know if you're a lower controller port and you spawn on a platform, you can hold down at the beginning of a set and drop straight through said platform. It gets predictable if you do it too much, but it can help you avoid those starting knees, especially if you drop through with a uair or something.
In general, it looks like your combo breaking DI is off. In a lot of situations, it looks like you're holding up at percentages where a knee probably wouldn't be thrown, just because it wouldn't kill you. That enables them to combo you more, which is bad.
I like where you're putting yourself on the stage. It's a good place to dash dance camp, although, sometimes, Falcon will go through you and literally corner himself by the ledge. Sometimes you move in, which is good, but sometimes you run away. That's bad not only because you lose that opportunity, but also because Falcon is faster than you are and it's fairly easy to chase you down if you're moving that predictably. So, watch that.
Also, I feel like you could be doing more off of your grabs. Falcon's a fast faller, but he's not a spacie, so your usual uthrow stuff won't always work on him, though it seems like you figured that out. Uthrow fsmash does work at some percentages and it looks like you took advantage of that once or twice, which is good. Your tech chases off of the dthrow are a bit lacking, though. Maybe consider cutting out the following dtilt if he's not near the ledge, since it looks like he's escaping quite a bit.
Make sure you know when to use the nair and fair. There're occasions where you'd use one where I think you should use the other. The nair, I feel, is more of a safe, defensive move. In most situations, I would rather connect with the fair as it tends to combo better, using the nair only as a sort of "stay off me" move.
Uh, ledge stall. You really want that invincibility.
Try to cut down on the random fsmashes. Dtilt stuff on the ground, utilt stuff in the air, ftilt if you really have to. Most of your fsmashes are aimed at Falcon when he's got half or more of the stage behind him, which makes it so you not only won't kill him, but likely won't even get him off the stage far enough to edge guard. It's damage if you connect, yes, but you could be doing more off of tilts and if he punishes the fsmash... well, combos hurt.
That's weird. The Falcon seems to always tech through you on the dthrow. You should be reading and capitalizing on that.
Try not to double jump or really, be above Falcon at all. His uair is fast, has range and combos. You don't really want to set yourself up for any more punishment than he already doles out. And anyway, you're Marth. You need that double jump for your recovery. So save it. In most cases, a Dancing Blade can substitute the double jump at much lower risk.
When you're edge guarding Falcon, space yourself out at tip range. Not only will this make your edge guarding hurt more, but it'll also help you avoid the Falcon Dive. You really need to make edge guards count.
Grab after dtilts. That's. Yeah.
Be patient. This isn't the best matchup for Marth, so really, be careful. Play the match on your terms and tempo, not his.
Ref Code: niko
First of all, pick a better ref code =P If you Ctrl-F "niko", it's all over the page.
...maybe it's the lack of audio, but I swear that first video looks just a tiny bit sped up. Weird.
Anyway.
Stay in your zone. Every time you're forcing yourself into his side of the stage, you're getting punished. Also... don't use the dash attack as an approach. It's really not that great.
Falcon has much faster vertical movement than Marth does and against a character that punishes as hard as he does, you don't want to leave yourself open. Ideally, you want to stay at short hop height or lower. Trim down the excess movement.
Speaking of movement, you really really don't want to be wavedashing anywhere near Falcon. There's even an audio cue on the wavedash that just screams to be punished.
For the most part, it looks like you're getting punished because you're getting anxious. You're likely missing edge guards for the same reason.
Simply, don't.
Yeah, you're playing against a pro. So what? They're still human and they're still limited to their character. They don't have an instant kill button or a never die button. Just relax, be patient and play your game. Don't be afraid to camp, don't be afraid to take your time. You've got nothing to prove, all you're trying to do is win through whatever means necessary.