I was told that it is possible to tell the coordinates where a photo was taken and the date and time it was taken. It is somehow embedded in the photo. I have three questions about this which are as follows:
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.
Images contain exif data which consists of various information such as resolution and camera settings. Some phones like you mentioned also save address coordinates into this exif data. The data can be read from images using a simple tool known as an exif reader.
When you are looking at the security implications of exif data, they might leak personal information which can be used to link photo's to a single phone or camera but rest assured that many social media (like Instagram, Facebook or Whatsapp) strip exif data from the images before uploading so your uploaded pictures don't actually have exif data.
In Windows, some of the metadata can be viewed via Properties > "Details" tab. It can be removed using the "Remove Properties and Personal Information" link at the bottom of that tab.
It is called exif data which is stored as metadata in photos, they can be used for digital forensic purposes. There are many online websites for example metapicz.com which will visualize exif data for a photo (not recommended to upload your personal photos on any website), You can use software for this as well, an example is exifdataviewer. For print screen images the same metadata fields are empty. You can delete exif data by using online tools or software (exifpurge). Read more about exif data here.
