Is it possible to manually alter initial values in a chess engine? I am curious of the games that would arise if I changed the initial  value of a knight to -1 or make standing on e5 worth -10 points.  

How would I go about to create such an engine? Is it possible to alter an  existing engine in such a way and let it play against itself?
Yes. You can download the source code for Stockfish here. Once you have done that you need to work out where the evaluation functions are and change them according to your requirements. Then recompile and run.