Is there no way to selectively delete images from a gallery or the server?
As far as I know, when the image is down voted enough, the image will be blacked out/hidden on the gallery like so:
So, making the 'hideScoreIfBelow' to a number like -1, will have images that are just generated- then downvoted, be blacked out. For 'deleting' the image, I don't think there is an option.
Do saved images remain on the server even if the specific generator is deleted? Does renaming the generator also reset the gallery?
I just tested this and the saved images are linked to the 'generator name' i.e. when you delete a generator that has images on it, save the name, create a new generator, change the URL of the new generator to the old one, it will show the old pictures from the deleted generator (this is may be due to it cached or will take a while for the server to delete the 'deleted' generators' data) so if you mis-delete your generator, you can still get the images back.
Renaming will also reset the gallery due to the images being linked to the 'generator name' (I think).
Are the saved images publicly accessible even if the generator is private?
As long as someone has the link to your generator, I think yes. Unless you save the images into a different gallery name which the user with the link doesn't know about, they wouldn't. (They also couldn't see the 'other gallery' unless they input the name into the gallery even if using the Browser DevTools)
Is there no way to reset the score of an image, or change your vote?
Yup, currently I don't think there is.