**If the aircraft is currently powered by the external Ground Power Unit (aircraft batteries not switched on), can I start the APU using only the GPU (without switching on the 2 aircraft batteries)?**
Yes you can as the APU needs only the DC BAT BUS for starting which is energized with the aircraft power network on GPU.
And here is the starting procedure reference with the external power
49-00-00-860-008-A.
I recommend reading it if you have access to the AMM.
**If yes, will the APU take over the supply of electricity to the aircraft from the GPU? Or will the GPU remain the primary supplier since the GPU has priority over the APU in supplying the 2 networks (AC BUS1 and AC BUS2)?**
GPU has a priority over the APU.
The priority logic is: Onside IDG> GPU> APU> Offside IDG.
**Is there any situation where the GPU supplies one AC BUS and the APU supplies the other AC BUS?**
No as both require both Busties to be energized hence paralelling occurs which is not allowed on the A320.
I hope I answered your questions.