It definitely looks like movement is a big problem right now. You don't want to be pinned down by Falco as that totally opens up his pressure game.
Right now your movement is really reliant on rolls. Rolling is extremely punishable on read and still leaves you open on reaction in some cases. Try to keep those to a minimum.
I would suggest going to the lab on battlefield, and practicing your fundamental movement options. Try to do at least 30 minutes of movement practice a day (minimum) and get used to controlling your space without rolls. A combination of wavedashes, dash dances, Wavelanding on platforms. Perfect Wavelanding until you can glide smoothly from platform to platform in big showoffy loops around battlefield. Come up with different patterns until you know every trick for getting exactly where you want to be.
Then put a cpu on 6 - 9 and try to avoid his attacks without rolling, but also without just flat out running away. Pick an ideal spacing (let's say a little longer than marth f-smash range) and try to maintain that spacing the whole time.
Then go watch pro matches to see how they control their neutral space. Like flippy was saying, try to see how they move around deliberately and aren't just spamming dash dance or something. Plup has an outstanding neutral game and I would recommend watching him closely. He has some excellent matches against spacies. Mango, westballz, porkchop.
Final thing, stage choice. Some of this is probably my preference. For first match I would probably try to strike to battlefield, avoiding final destination, fountain of dreams and Yoshis. FD is just combo hell and he can laser camp you all year. Yoshis is being favored for the bird more now that Falcos are learning how to take advantage of the stage. If you can't get battlefield, I would say dreamland as you have room for needle play and camping platforms to avoid pressure.
Until you can tech chase exceptionally well, I don't feel you have as much to gain from yoshis and fountain of dreams, and may do better with more room to control your space and avoid his pressure.
TLDR: sorry I'm long winded. Learn better movement and pick better stages.