Hmm... I don't have any Foxes that are specifically good against campy Falcos. I'd just watch Foxes against Zanguzen, since he's the most notorious campy Falco.
In terms of your problems specifically, here are some things to think about:
Lasers:
The classic answer is to powershield them, but I think that solution isn't necessarily the best given the difficulty of execution and the frames spent actually performing the powershield. Frame-perfect powershield > wavedash takes 21 frames, while Falco lasers stun for 12 frames. You get the benefit of the laser returning to Falco and discouraging him from spamming them, but I wouldn't recommend it as the first solution that you try to implement.
Simply reflecting them back takes 38 frames, which is a long time. Again, you have the benefit of laser returning to Falco and at least forcing him to avoid it. The only time I'll bother with the reflector is when the Falco is spamming lasers from far away and you don't have access to platforms. This can usually get them to at least stop spamming lasers from full-screen.
PPMD recommends just eating the lasers and learning to move out of them, which sounds a bit counterintuitive, but is actually a really good option. Falco's lasers stun for 12 frames, so unless Falco is hitting you with a low laser from very close, he doesn't get much frame advantage. Unless the situation is near-perfect for him, theoretically, Falco isn't guaranteed anything from laser approaches. Additionally, you can crouch-cancel the laser and cut the stun down to 7 frames. Crouch cancel also starts working on the first frame that you input it. I'd highly recommend that you practice moving out of lasers as fast as possible, regardless of whether you're CCing them or not.
Platforms are also a great tool to combat lasers, especially spammed ones. If Falco follows you up, just run off and take center stage. It takes him a long time to jump to a platform and get a laser out, while full-hop lasers are really tough to hit Fox with. If he stays grounded, just use the platforms to close in on him.
Crouch-Cancel Shine:
Approach this the same way you would any other crouch-cancel spamming character, i.e., Peach. Shine, grab, and drill are all great answers. If you're not using those moves, try to space your other approaches outside of his shine hitbox (which is much smaller than Fox's, by the way).