-We do have a chaingrab on Falco.
-Basically it goes: grab -> at least 1 pummel -> grab release -> buffered boost grab -> grab -> repeat
-As for our camping game, I like to pull out a nade, jump higher than the peak of his full-hopped laser, throw the nade from there, pull out another nade and shield to make it fall on top of him. He can't reflect what's above him. Crouch if he's spamming lasers and time the correct time to jump.
-Or just do what Bizkit said and cook them for exactly the right time.
-Get Falco offstage. If you see him use his jump and he's still below the edge, go for the gimp ASAP, he's going to use his upB.
-If there are platforms anywhere, camp them until you're at about ~40% and use safe moves when coming to the ground. I use this strategy with Wolf too. If you're on FD, keep as much ground behind you and Falco as possible.
Counterpicks:
Lylat- Stops his laser game to an extent. Try to stay on the lowest side of the stage when it tilts. Your mines/C4 are hard to see. Keep track of them.
Frigate- Falco can't camp as much on this stage and his recovery options are limited when the stage is missing ledges to grab onto.
I usually go Frigate just because I love that stage.
Ban priority:
Japes- He can pretty much camp a platform on the edge, and if you approach him, he can predict your landing pretty easily on the platform. The ceiling is ludicrously high, which makes uptilt a harder option to kill with. If he chaingrabs you, a good Falco will get you in the water and possible Croc will kill you. Phantasm leads to instant grabs on the outer platforms.
FD/SV- Whatever you feel least comfortable on.
Ban Japes if it's legal.