Is it possible to spot photoshoped or edited photos using AI? I have this question in my head: does the current level of AI development allow us to spot faked or photoshoped images? (i.e forged ID card or personal documents).  

If it is possible, what is such a process to follow in order to build an AI that achieves this task?
It is possible! Here is an article by Adobe where they explain how they do it: https://theblog.adobe.com/spotting-image-manipulation-ai/

The algorithm for this would almost certainly be a Convolutional Neural Net trained on a dataset of real and manipulated images (labeled as such).