As far as the computer turning off is concerned, look in Settings > System > Power & Sleep to control when the screen turns off and when the PC goes to sleep. There is also a link here that provides additional information. This is not the same as lock screen found under Settings > Personalization > Lock Screen.
On an aside, there has been discussion elsewhere in the forum of potential problems arising from use of sleep mode and hibernation.
Regarding the problem of the Lock Screen Slideshow not finding your photos on your external drive, it may have something to do with the Environment Variables or entries in the Registry, but I don't have sufficient knowledge to provide any detailed information.