Aside from some spacing issues (such as not positioning yourself far enough away from the ledge to prevent Sheik from rolling behind you when you try to edgeguard her with Flamethrower), and not using Charizard's best and most defining move, Flamethrower enough, I do not think that you made many outright mistakes in those matches. There is nothing you can do except gain more experience and practice if you wish to defeat an opponent who can outmindgame you more than you can outmindgame them.
Anyway, here are two matches I had against some exceedingly tough opponents:
I don't really feel like I'm having problems with the mindgames though. Everyone and their mother knows Shiek is going to approach you with SH fair or a dash grab or just toss needles. Neutral is where Charizard (and therefore I) struggle the most. Mindgames out of Dthrow are an issue but I think that our neutral game is a far larger problem in that MU. We don't even have good options to use in neutral and Sheik has 3.
Am I supposed to throw out jabs at the aerial approaches? Do use jabs after I shield Fair? How often am I supposed to use Dtilt? Should I be using Ftilt as an anti-air on Sheiks short hops? Is SH Fair even worth using as an approach considering how easy it is for Shiek to punish on whiff? Did I misuse or neglect to use any good options, essentially.
Also Flamethrower is kind of ass in that MU. If Shiek reads it and hops the flames, you get carried away by Fairs. If Shiek mashes bouncing fish, you lose the trade. If Shiek shields, she straight up picked the wrong option. Best case scenario is you cut the flames early and you bait+punish a bad bouncing fish. What if she doesn't bouncing fish though? What if she just tosses/charges needels during your lag or resets to neutral? You've only succeeded in annoying her and you don't get a fresh Flamethrower for potential edge guards. Not worth.
Anywho, thoughts about your games:
Dtilt is really good in the Luigi MU; you should use that a ton more. It's way safer on whiff than jabs (he got a dash grab after some missed jabs) because you can usually jab Luigi before he gets to punish. Just don't do it when Luigi charges an Fsmash because he can hit you on the way back. I'm pretty sure it clanks with a ton of stuff too. It also covers rolls way better than jabs imo. Especially after that buff. It's also safe in shield because Luigi's traction is awful.
Also consider using Utilt after people shield your Nair while on a platform. It covers OoS jump really well but sacrafices some of the horizontal coverage that Usmash provides. Luigi didn't seem to be jumping away from Usmash though so you were using the right option. It's just something to remember.
You should also probably consider stopping your jabs after Jab 2 when they whiff. Maybe not all the time, but if you want that last jab for its range, youre usually better off just using F/Dtilt anyway. It's also harder to punish on shield/whiff if Luigi doesn't know when you are going to stop jabbing. Faster characters sometimes get to you either way but they at least run the risk of dashing into your third jab if they try to punish jab 2. This keeps a lot of people at bay in my experience.
Also definitely shield Link/Tink's projectiles. They aren't like DHD and Dedede who can actually move and damage you a lot while they have strong hitboxes floating around on the stage (in which case, you're very often better off avoiding rather than shielding so that you can avoid the opponents normals easier). They have some bomb setups but that's about it. Tink also has a hitbox on the return part of his boomerang but if you just shield the first part, you have nothing to worry about. These characters really can't act independently of their projectiles so just shield them and move on. No need to jump and stuff for those MUs, generally speaking. Certainly don't jump over projectiles shot from a distance.
Exciting matches for sure. You might want to mount that camera next time though.