I dont play dr mario but I play falcon so im gonna say a few things about that
first of all, really nice combos by falcon. And very nice movement, the dashdancing is very fluid.
Both of you have very nice/good movement. You know what you're doing. Nice up-b cancels btw lol.
I think you need to work a little bit on your get-out-of-combos di though, fire ghost.
Try DI'ing his nairs and uairs down and away. He can still follow up if he's fast enough but it gets a bit harder.
As for his grabs, DI his dthrow down and away for the most part (looks like you are-good) cuz it makes it a little harder for him to follow up
At very low percentage (0-20% or something) you can actually DI his dthrow up and towards falcon-this will bait an uair which doesn't combo at low percent, so you can jump away.
btw, if you're high up in the air and goes for nair->nair combos you can DI up and towards falcon, that way you might only get hit by the first hit of the nair so you can jump away. But this type of DI is very situational and you must be very careful about using it, b/c if you di up and he knees you you'll get double/triple knee'd. He can also just uair you.
Dr mario can basically get comboed to death by falcon regardless of how they DI btw, the di i suggested here is far from gauranteed, just a few things that can mess him up.