Hey Jan,
you will get an ID at the Civil Status Office in Victoria, Independence House (Same office where you will get the GOP). They will take a photo and print your ID right away.
The local driving license has to be obtained within 3 months. You can get it at the Seychelles Licensing Authority, Ground Floor, Orion Mall building Victoria. Same as with the ID, they will do the snap right there and print your local driving license. Just bring your foreign driving license, as proof that you know the difference between accelerator and brake pedal )))
Cheers,
Peter