Movement is great, learn to USE it though. If you can run around so well like that make sure youre doing it to mindgame into grabs.
Fox and Falco are about PROXIMITY. Keep close and on top of them, but not close enough for them to hit you. You just want the spacie to feel VERY pressured.
Your nairs seem fine, just your follow ups could use some work. Nair > Grab at low %'s. Nair > Stomp at mid/high so you can punish missed techs.
Your follow ups in general seem like they could use some work, DON'T RUSH YOURSELF!!!! I know you wanna punish the **** out of him, but be sure to take your time. I see you Dthrowing and not even thinking about the situation, your move choice is a little off. You'll Dthrow and then just instantly go for a spot dodge knee off your first grab. DON'T!
If you grab him and dthrow, he has 4 options. Tech in place, Tech away, tech twords and NO TECH AT ALL.
Hes going to probably tech so be aware, and a tech in place isn't very likely unless he has the momentum in the match. So grab, and wait for him to tech away or twords and then get the grab again. Doing this will force most fox players into teching either in place on the 2nd throw, or the oppposite of whatever way they teched.
If he techs in place, punish with a knee or stomp. If he techs the opposite way he teched on the first grab, then just regrab/knee. RAPTOR BOOST IS YOUR FRIEND AFTER THE FIRST DTHROW AND WILL COVER ALMOST EVERY OPTION IF YOU RUN BEHIND HIM THEN RAPTOR BOOST THE OPPOSITE WAY. It'll hit his nontech and chase his tech behind you.
I don't see any uthrows. Learn to use uthrow as a mixup at mid-higher percents, many players panic and will miss the uthrow tech or will make it more obvious which way they are going to tech because you can see which way they are going to DI a little longer. Not only that, but I saw you can gentleman quite well.
Uthrow>gentleman mixup will ALMOST ALWAYS GET YOU A KNEE OFF A MISSED TECH.
Gentleman more on his shield when you're keeping proximity and trying to pressure him.
I think you're on the right track though, good looks man. You have your fundamentals down, its the small things that you seem to be having trouble with.