Okay, I'm gonna watch the Fox match. Falco is a weird match up.
I dunno why you're not fthrow regrabbing. He's not really spotdodging to avoid it, and it's free damage at really low percentages.
At 1:05 you shoulda gone for the uthrow chain grab, because the utilt isn't really going to do anything at such low damages.
It's probably not that great of an idea to charge the Shield Breaker as an edgeguard when Fox isn't that far out and you're on Battlefield. It locks you in place and severely limits your options. If you just move around and keep mobile, it'll turn out much better for you, as he'll pretty much be forced to go for the ledge or else eat an fsmash.
You're missing a lot of the fsmashes on the platform. Honestly, it's generally not the greatest thing to go for especially when they're in a neutral stance, unless you're trying to get the kill, as they're pretty easy see coming and to avoid. Try utilts or uairs or waiting for them to roll or spotdodge before going for the fsmash.
For the Counter edgeguard, you're going to have to go right up to the ledge so he doesn't go straight up past you. Also, don't get nervous on the edgeguards. Use the dtilt if you're not sure so you don't get so much lag, and that way you can try again before they hit the ground.
After the Counter, you need to go down for the fair gimp, otherwise they're not going to die for a while. It's an easy kill and you don't want to keep having to try the Counter, because they might get around it and then you'll lose the kill.
Yeah... watch out for that shinespike.