1) Falco is going to try to CG to spike you when you are under 40-50% damage. To avoid this you need to keep bananas around you and work on your spacing with dribbling/other methods (Aeriel movement). On top of this DO NOT stay in the center when you are under this damage threshold. You need to zone to the side 1/3rds of the stage so that if he does grab you he can only land 1-2 down throws instead of 4-5 downthrows (so you eat 30ish damage instead of 50-60ish).
2) If he does land the CG he will try to spike you. There are two things to know about this spike: if he spaces his CG wrong (though its actually complete chance because the spacing is set based on where he first grabs you) then you can DI the down air INWARD so you hit the stage and you can try to tech that. This is probably the more risky option though. The second option, assuming he spaces the CG correctly, is that you need to wait about a second, use your second jump AWAY from stage, then charge your barrels. Using the second jump away from the stage gives you the option to either shoot for the edge or shoot for above the stage. Sometimes as a mix up you should just jump straight up and not away from the stage, but that is only if you think the Falco is going to be aggressive and attempt to gimp you even further (aka by jumping straight up you can do a quick up-b without having to charge and angle it). If you get caught under and inside the stage you are basically screwed, if you watch my winners finals match against him I make this mistake on the very last stock (sigh). It was the only time he managed to land CG > spike on me.
Doing these things will make your Falco match up significantly more easy (though still sucky).