If a photo is taken using an iPhone, the image file can carry date, time and location information. If this original image is then screen shot, would this original information be copied with the screen shot
No, it will not.
Information such as time, date, author, etc. is stored as EXIF metadata. This data is kept separately from the image itself, and as such will not be retained if you take a screenshot of that image.
You may be thinking of steganography, which is the process of hiding information in another piece of information. The Wikipedia article offers an excellent introduction to the topic, along with an example of what it can do.
This can be used to hide information in the image itself, but EXIF metadata isn't stored this way.