Regarding guns and planes, unfortunately, I don't know. I've only shot in the Netherlands and Germany and we can get there by car. I will also go to the UK by car, and one of the reasons is that's it's not that obvious to take a gun with you on a plane. But many shooters on the Worlds in Germany last year came by plane, so it's definately possible.
About the papers you need, I'm not sure either. I have all my guns, including my airguns, on a European Firearm License so I am allowed to carry my guns through the EC. I need this for example for Germany as only 7.5 J airguns are free there. In the UK, the limit is 12 fpe so in theory you don't need a European Firearm License there if you gun is 12 fpe (and it has to be for the Worlds), but the UK law says a airgun should not be capable of exceeding 12 fpe. If you set your PCP close to 12 fpe with light pellets, the gun will probably be over 12 fpe with heavier pellets and you would need a license for it.. So to be absolutely sure, I'd get the European Firearm License.
Although I'm doing not too bad in Belgian and German FT-matches, I'm not match for the British shooters. So I don't go to the Worlds with high expectations, I'll be happy to end in the top 100 and even that will be difficult. My objectives are not to end last
I hope to see you at the Worlds
Mario