There are a few technical things you should be aware of.
Firstly, shorthopping your aerials is very important, as I'm sure you would notice in the first few seconds of the video. SHFFLing is a little harder to pull off with Pika than with many other characters but used with nair it can be very useful.
Secondly, remember to jump cancel your grabs. I wouldn't recommend running up for a grab with Pikachu anyway due to his terrible range, but if you're going to do it then it's important to minimize lag as much as possible.
Thirdly, to avoid Fox's uthrow-uair, you'll have to DI away from his hits, which is explained more fully
here. Kind of hard to understand/pull off at first so if you don’t get it don’t be discouraged.
Be careful with your thunder jolts. You don't want to shoot them out too close to any character, and Fox's speed means that he'll be able to capitalize on your ending lag extremely well.
I know it doesn't seem at first like you have to l-cancel nair but every little bit helps.
Make sure your quick attacks head straight for the ledge (in most cases, unless someone's edgeghogging or something) as they are much less punishable that way.
I wouldn't recommend going far below the stage to edgeguard until you get the quick attack mastered. Sometimes easier edgeguards will work, like just waiting on the side of the stage to fsmash, dtilt, or ftilt them back out. Just make sure you don’t get too predictable.
DI away from Falcon's throws and upward attacks so that it's not so easy for him to land his knees.
The biggest thing I would have to say is not to go for grabs so often. If you can combo into a grab or punish their mistakes it's a different story, but you just don't have the range to enjoy the luxury of running up and grabbing them. This ties into what N64 said about mixing up your approach.
Keep at it