Q: Are there any flights from Girona to Seville airport (SVQ)? Are there any direct trains or buses between Girona airport (GRO) to Barcelona airport (BCN)? How long does the transfer take?
A: There are no directly flights from Girona Airport to Seville. You would need to go to Barcelona airport and fly from there to Seville.
There are also no direct transfers between Girona airport and Barcelona airport. At Girona airport you would need to catch the Barcelona Bus operated by Sagales and get off the bus at Barcelona Nord bus station. The travel time is about 1 hour 20 minutes. At the Barcelona Nord bus station you need to take the Metro Metro: Plaça Catalunya. At Plaça Catalunya you can catch the airport shuttle bus Aerobus. Alternatively just take a taxi to the airport when arriving to the Nord station.
You should always bear in mind additional transfer costs when working out your itinerary. If you bear in mind the cost for these on top of the flight. It may be worth paying a little more and simply fly directly to Barcelona Airport.