GSP IS a Jedi. Who says he isn't? He is just not the same Jedi as Anderson is.
Anderson is more like Anakin Skywalker. Eager to finish off the opponents. GSP is like Obi Wan Kenobi. Patient and does only the absolute minimum to make sure he wins. He doesnt like others suffer unnecessarily :-)
Nope. GSP is not even close to Jedi. Hes never done anything that can even be remotely considered Jedi. A superb fighter he is... but not Jedi.