The Royal Canadian Mounted Police are shown checking baggage in the final scenes at the same time that FBI agents are making arrests. The flight landed in Goose Bay, Newfoundland and Labrador, Canada. According to the Criminal Code of Canada, any crime committed during an international flight that ends on Canadian soil is deemed to have been committed in Canada. That being the case, the RCMP as the national police force has full jurisdiction. There is no way the FBI would be involved at that point.
The role of Kyle was originally written for a male character, but when Jodie Foster expressed interest, the filmmakers felt she was strong enough to carry the part and cast her instead.