The iPad's native Photo app cannot create folders and it cannot delete photos that have been synchronised with your PC. To create folders this needs to be done on the PC and then a sync. Similarly, to delete photos that were sychronised with the PC, they need to be deleted from the PC first and then synchronised again. Photos that were not synchronised - say they were received by email - can be deleted in the Photos app.
Most members use a third-party app; these enable you to create folders/albums, delete photos and organise them any way you want.
Tim