Can't delete iPhone photos or transfer to PC

Probably you have synced these Photos from your Mac/PC through iTunes, hence you can't sync these back to PC. Un-sync, then they would be gone from iPhone.

UN-Sync photos to your device

1. Connect your device to your Mac.
2. You can connect your device using a USB or USB-C cable or using a Wi-Fi connection. To turn on Wi-Fi syncing, see Sync content between your Mac and iPhone or iPad over Wi-Fi.
3. In the Finder  on your Mac, select the device in the Finder sidebar.
4. 
5. Select Photos in the button bar.
6. 
7. Note: When iCloud Photos is turned on, no photo syncing options appear when you select Photos in the button bar.
8. Select “Sync Photos to your device from” tickbox, then choose Photos, Pictures or a folder from the pop-up menu.
9. 
10. Uncheck Sync photos
11. Click on Apply / Sync