Raven
Corn!
Lady Blackfyre: you're correct.
The Citadel: So Spake Martin - Eastern Cities and Peoples
Fourth: Illyrio is noted as having ships that trade with Westeros - in fact, we are obligingly given the detail that he even travels on these. (Salladhor Saan captures a ship that belongs to Illyrio in ASOS.) So he could easily have popped over to KL.
As for your questions about Illyrio's motivation, some of these will be addressed in ADWD.
The Citadel: So Spake Martin - Eastern Cities and Peoples
Fourth: Illyrio is noted as having ships that trade with Westeros - in fact, we are obligingly given the detail that he even travels on these. (Salladhor Saan captures a ship that belongs to Illyrio in ASOS.) So he could easily have popped over to KL.
As for your questions about Illyrio's motivation, some of these will be addressed in ADWD.