Sheik forums need to step it up.
I watched the two matches vs the Falco. You have the tilt -> slap combos down pretty well. That's good. However, you seem to have trouble following up tilts/dash attacks when they put Falco on a platform. It's fine to try to just hit him if he misses the tech (which was usually the case). But just in case he techs in place, it's better to time the fair so it hits him after his tech animation completes. That way, your attack won't miss due to him being in the tech's invulnerable frames. By making a habit of this, you will always cover two options at the same time.
Your spacing is solid. Most of the time, when he tried to hit you with an aerial, you got around it and punished. It's good to be competent in this department, because when people first get into the competitive scene, they tend to get run over easily by the super aggressive space animal styles. But I see you can keep your cool. Very nice.
It appeared that you have a reasonable grasp of Sheik's edgeguarding tools. I feel like the main reason why you let Falco recover a lot is because you kind of played it too safe. Whenever you hit Falco below the stage, you should always drop down immediately and fair him. It works every time. I remember one time you went for the fair and got hit by a firebird. But I think you might have hesitated before going after him, and losing that time was crucial. It doesn't matter what the angle. It should be mechanical. Falco drops below stage without his second jump ... drop down and fair him. Don't even wait for his firebird to charge up completely (although it's entirely possible to hit him as he's moving). His up-b has no hitbox, so there's nothing to worry about.
Also, try to cover as many options as possible when edgeguarding. When Falco is offstage, he'll typically be able to recover the quickest via his side-b. Always assume he'll go with the side-b right through you first. Prepare to ftilt/dsmash. You should position yourself as close to the ledge as you can before he takes action. If he jumps and it appears that he'll side-b over you, bair/fair him if he lands on a platform. If he goes over you and lands on the stage, it's all situational. Bthrow if he's still close to the edge. Ftilt -> fair him at higher percents. If Falco doesn't side-b, but instead up-b's, you should be able to find a good way to meet this decision, since the up-b takes so long. Edgehogging -> bair/nair is usually the best in this situation.
Hope this helps. Good luck.