the coordinates where a photo was taken and the date and time it was taken
It's called EXIF metadata. It depends on the camera, or phone, or application. Digital cameras usually save the image parameters (f-stops, ISO, shutter speed, etc) on that area. Cell phones can be configured to store coordinates too.
Where is this information stored? Can it be deleted?
This data is stored on a special section of the file, and it does not change the image in any way. It's just a special text section that can be read/written by special software. It can be edited and deleted as well, and even contain fake/falsified data.
Deleting this data is trivial. There are a couple programs that removes that data in batch. Exifpurge is one, exiftool is another one.
is it the same for print screen images?
It is the same, as EXIF headers are part of the JPEG specification. As most of the EXIF fields are not relevant for a screenshot application, most of the fields will be empty. You can test your screenshot application by saving a file and submitting to a EXIF metadata viewer, like this.
I am not aware of any image editor software that embeds coordinates on the EXIF headers by default.