-Unless you are able to set up an edgeguard with f/bthrow, always downthrow fox. ESPECIALLY at low percents.
-Too often a light shield came out after your wavedash. This means you are holding l/r for too long.
-You make good use of fair off of platforms. Often when you and fox both had an equal amount of stage, you would go up to the platform, he would try and take stage by going under you, and you would fair him for being aggressive. This is good and worked multiple times, but I have two recommendations...
1) Be cautious of jumping to the platform when fox is close to you. Being under Sheik is a very favorable position, and if they hare close enough to you they can take this control before you have time to punish them for moving forward. Save this option for when he is at safe laser distance, or if you are backed up to the ledge and have to take a risk;
2) Try to mix in needle grabs from platforms too. Needle grab will give you a much larger punish if you read that the opponent is going to try to encroach on your space, however fair is a much safer option. In general, Sheik's fair in this situation is safest because you can AC and dash back, ftilt, dash attack, grab, etc. almost immediately after landing. But if you see them try to take stage, let the needles fly.
-Work on tech chases. We all need to do it.
-1:49... wut? Haha, I get that you thought he was going to illusion back onto the stage, but upsmash is not a good edgeguarding option with Sheik. Even if you had guessed right and he had illusioned back, it would have made much more sense and been much safer just to ftilt>fair. Don't go for upsmash near the ledge. The risk/reward is just not worth it.
-SH AC fair is AMAZING against Fox. However, not in the way you were using it. Approaching with sh ac fair is very very unsafe, and doesn't require a read to punish. As soon as you sh towards your opponent, they can punish you on reaction, and the punish is going to be brutal since Sheik has so few options when she is above her opponent. The way you should be using sh ac fair is retreating. Dash in, sh backwards, ac fair. This is soooo safe. Assuming you spaced the short hop correctly, spacies can't punish the fair without getting hit by it. So basically, either you hit them with the fair, or you land with a bunch of empty space in front of you. Once you land, if the Fox has tried to dash in and take the space that you left, you can grab, dash attack, ftilt, etc. from a safe position. You could even dash back>pivot/crouch/dd to open up a whole new world of options. If the Fox respects the fair and doesn't encroach on your space, you can just dash forward and reclaim the space that you gave up FOR FREE. Too good. Use this. Plz.
-The key to the Fox MU is to make him respect your space. If Fox can just be in your face non stop you are going to lose, period. Make him feel unsafe when he tries to get close to you, and you will have the upper hand.
I only watched the first match fyi, but this is what I observed. All in all it looked pretty good. You didn't throw out a ton of stupid punishable moves (there were some, but there always will be some) and you made Fox respect your space pretty well.