Obviously you need to grind in your movement skills as much as you can, as a fairly new falcon (been playing for like five months) i still have some trouble with my movement sometimes and i myself should do this too.
movement skills meaning you should work on wavelanding, and dashdanceing. i dont find myself using wavedashing that much playing falcon. i tend to only use it to help with spacing, getting out of shield, and ledgehogging. dashdancing and wavelanding are probably some of the more important skills you need to learn for falcon in my opinion. also work on perfecting L cancelling if you havent already.
for falco combos all i can say is that no matter what your going to do your probably going to get bopped by any falco that knows what they are doing, its by far the hardest matchup for falcon. but i will say you should shnair over the low lasers and raptor boost under the high ones. (also an important tip, raptor boost has a wide frame opening where you will just pass through lasers even if they look like they should hit you. keep that in mind.) try to stay close enough to falco to raptor boost him but not close enough to get destroyed by his insane neutral game.
as for counter picking, learn what stages are good for falcon and try to evaluate stages for yourself. falcon tends to really like large stages, because they give him space to move around with. dreamland 64 is personally my favorite stage for falcon. fountain of dreams is my least favorite. also note that you can FH stomp THROUGH some platforms. this works on battlefield, pokemon stadium, and fountain of dreams. one more thing about stages, when you find yourself on a platform with the enemy at your level, dont just run off the platform. as you fall from the platform you should throw out a uair or some quick areal so you can have a hitbox out. obviously l cancel it when you hit the ground. if it hits its a possible combo or momentum breaker for the opponent.
i could go on and on and on but this is already a lot for you to digest. write this stuff down in a note book or something, it will be better than having to remember all of it. and after you take note of everything here go watch some falcon videos and study some of the things professionals do, look at how they got that super flashy cool zero to death combo. look at what percentage they waited to upthrow knee their opponent. things like that. after that just look around smashboards and ask more falcon players for advice and more tips.
GL on your tournament, and dont feel down if you get bopped hard. everyone goes through their first tournament experience. even the pros.