1) You don't suck.
2) Hooray! Up-throw forward-smash!
Hmm... Lucky clearly has the IC matchup well in his head, so it's not any shame to be losing to him. But obviously you want to win, so I'll try to focus on that.
Fighting Fox is a lot like fighting Peach in that a lot of the time your punishment openings are just illusions. Fox is not open very often, but the desire to stop his offense is really strong; you've got to resist the temptation to attack whenever you think there's an opening. Pressure that opening but don't commit (since it doesn't exist) and bait a response. Punish that instead.
Also, try not to be above him, ever, if you have a say in the matter. Spaced b-air and f-air is fine while falling, but it's really situational and if Fox has time to move around he can dash dance camp and regain ground momentum. Overall, stay low.
Also, hit down the moment you fall off the ledge from being shined; you'll grab it right away (even if you get shined near it) and you can start retaliating when Fox follows up. If he runs off to gimp Nana, you could probably just hit him; at any rate, it's better than being shined.
Also, for fast fallers I prefer b-throw or u-throw with SoPo. B-throw has better tech chasing (IMO) and u-throw lets you smash, dash attack or chase around platforms, and when fresh it does 11 damage, which is better than the 5 you get from d-throw and b-throw. B-throw is harder to react to and certain DIs make it harder to tech, which lets you wavedash jab or d-smash. If you grab in the middle of the level, forcing the enemy near the edge, especially a fast faller, gives you a really big advantage from a grab.
And since we're talking about grabbing, when you have an opening (especially when sync'ed), grab grab grab. If you grab Falcon near the edge, he should die. If he's at 80 when recovering and lands on the stage, unless you're SoPo or you're terribly de-synced, you need to grab. Even if you don't CG, a fully charged d-throw f-smash does more than a d-smash and has more knockback, so it's always worth it.
U-air b-air is very situational; you try to use it a lot, but it requires hitting with the end of u-air. Against fast fallers at mid-percent you probably want to u-air d-air or u-air into falling u-air--they combo better and tend to have better follow up.
The shield-belay edgehog is really cool looking and lets you stay on the stage to act, but Nana acts immediately from the edge and it leaves you vulnerable for a substantial amount of time--in short, you get less edge control and you're more open. I personally wouldn't use it for anything but discouraging a space animal's forward+b, or looking awesome. It does look awesome.
As SoPo against Fox/Falco, you can edgeguard up+b pretty obnoxiously with repeated ledge-hop d-airs. If they're below the level, ledge hop d-air and poke the spacey's up+b making him redo it. Quickly wavedash back to the ledge, then ledge hop d-air on the up+b again. You'll build damage and eventually force a bad up+b spacing. If they try to DI away and then change the up+b pattern, you'll be able to edgehog, b-air, or land on the stage and d-smash them. It's kind of protracted and difficult, but it uses less prediction than a normal edgeguard or edgehog--it also gives them the chance to randomly kill themselves with air-dodges, accidental forward+b, or just a really dumb up+b if they panic.
Another thing to remember about Fox and Falco is they often love going to the edge with up+b from above. In general, you should face backwards when edgeguarding; it lets you edgehog faster, punish forward+bs easier, and if you have to, you can always just turn around. Also, for forward+b, try CCing at low percents then grabbing. CC grab is my new go-to punisher, in case nobody's noticed.
Lastly (and I know this is hard when playing in tourney) you have to really focus on certain key moments; when Fox dash-attacks your shield, you have to quickly think "has he crossed me up?" 99/100 times he hasn't because you slide backwards and ICs have a powerful reverse grab, so you typically get a shield grab. When you land a dash-attack at low percents you have to think "grab." You need to create... mental subroutines, I guess... that just run automatically under certain circumstances. For instance, building damage with tilts or blizzards when you get a grab before you CG. I've picked up the bad habit of just doing a single headbutt in between CGs when I could be doing tilts or blizzards--it means I have to repeat the chaingrabs more often and that creates more chances for mistakes.
So basically, you need "moment awareness." Some clutch moments and openings require you to really be attentive--you could have beaten Lucky and Mango in a few moments but it seemed like you didn't realize you had an opening. It happens to everybody and it happens in your mind, but you've got to try and improve it. Everybody does, actually.
Oh, and as for Falcon... you actually do really well; remember that Mango's a smart player--it's harder to learn matchups against really smart players because they tend to be unorthodox and adaptive to your actions. You won't often know if you're playing the opponent badly, or the matchup badly--personally, I can't tell in a lot of cases. You do well against his forward+b when you're able, but sometimes he just sneaks it in; whether you know it or not, I can't offer advice beyond "predict better" and that's kind of lame to say. From what I saw your matchup knowledge was decent, Mango was just outplaying you, and in Mango's case that's no dishonor.
So... I hope that helps? I also hope I'm not telling you things you already know.
Edit: Forgot Falco.
Fortunately you do a lot of stuff well and you handle his lasers pretty strongly. Again, you have to be cautious about trying to aerial when you don't have an opening but by and by it was pretty good play. And you need to grab more and more; u-tilt, dash attack, certain u-airs, they combo into grabs, and if you fully master the handoff + damage builders that should terrify everybody you play against.
