Can a service dog fly in the cabin of a plane for international travel?

Answer 1

That depends on the country of departure's laws and the country of arrival's laws. Some countries require all dogs, including guide and service dogs, to enter the country as cargo. Check Consular Information Sheets for the individual countries involved to find where to check the regulations for dog import/export. See the link below for Consular Information Sheets.
Yes, on flights originating and arriving at points in the U.S. or U.S. territories. The Air Carrier Access Act requires air carriers to permit service animals to travel in the cabin with their disabled handlers unless an animal physically does not fit in the space allotted to the traveler and there is no other space on board to accommodate them. If the animal will not fit in the cabin, the air carrier must offer to transport the animal as cargo free of charge.

Answer 2

Service dogs (such as seeing eye or hearing ear dogs, etc.) must be allowed on the plane with their owners (they may have to purchase two seats). The rest is up to the specific airline. Call the airline to find out or ask your travel agent. Some airlines will ship the dog in the cargo hold, but you need to find out exactly how long the trip is, what carriers are approved, and how cold the storage compartment will be, etc. to decide if that is the right plan for your trip. Some airlines will allow very small dogs in the cabin as a carry on in special travel carriers, but they will not be allowed out of the carrier.