Since the serie was cancelled, a lot of mysteries remains unresolved. I (Jasonx11) will try to answer it within the serie without guessing it. Otherwise we have to wait until Cage of Eden anime come out (hopefully).
Wonderful World arc
Q: What was the huge beak thing that attacked the airplane in mid-flight?
A: It is either an Argentavis or another flying bird that flew in the sky just as the plane came into the island range.
Q: Why does the beak appeared inside the plane?
A: During the turbulance the plane was probably caught between two realms: the future island and their present. Between the two realms both objects passed each other without any damage.