ZSS vs Metaknight:
This is ZSS's worse Matchup in my opinion; however, solutions are always present in every situation. You never want to be too close to Metaknight, since he can beat any option you can take. You should play Footsies with MK and try to poke him with your D-smash, Plasma whip, and Paralyzer. However, I'd use D-tilt more than D-smash since D-smash is slower than D-tilt hence can be punished more frequently and isn't as guaranteed as D-tilt. When MK uses nado on you, shield then Up-tilt OoS when the nado ends. Once MK is on the air, wrack up some damage with as many Up-airs as possible. When MK is gliding toward you or the stage, never feel discouraged to hit him with a F-air, the initial hit of F-air will clash with glide attack and the second hit will connect.
This method can be used as an edgeguard against Metaknight as proved by this video (time: 2:00):
Edit:
ZSS vs Falco:
First of all, you need to be careful with your suit pieces since Falco has a reflector. Remember that he can still use his reflector on your suit pieces while they're bouncing so that it causes a threat to you instead of him. Falco is prone to use his Lasers against you, forcing you to approach him. Just becareful of his grab, you can't DI out of it before 34% (iirc). Try getting a Dash attack > Up-tilt and keep him in the air, ZSS's aerial game is superior to Falco's. Catching Falco with D-smash is promising, since you can chain D-smash on a FF such as Falco, Fox, and Wolf, I'd usually go for 2xD-smash > 2xD-smash > 2xD-Smash > F-air which deals 83% damage if both hits of F-air connects (You can choose to use B-air, but I'd recommend F-air for extra damage if you can land it) D-tilt is a great option since it can't be punished if spaced correctly. If you get a D-smash on a Falco who has lost his SJR offstage, a footstool to edgehog (properly timed) is a guaranteed gimp. If he decides to recover with his Side B, you can try predicting his landing and punish it (either with a quick edgehog if he's aiming for the ledge or a D-smash if he's aiming for the stage).
If I can summarize this matchup, I'd say that it's about dealing with an annoying bird who jabs, lasers, and sideBs across the stage. It's annoying, just follow what I said and ask the top players (since they have more experience than I do) and you'll hopefully improve in the matchup.