Isn't the portrayal of psychology and intelligence too unrealistic?

First, about Will being a genius... I can believe that, but they never really show him a actually studying at the library. In fact, between being in bars, the batting cage, getting into fights, being on parole, his many jobs; I find it hard to believe that he actually has that much spare time to read that much. Einstein and other scientists known for being exceptional studied a lot throughout their entire lives, and they were mostly aware of their intelligence since they were kids. Furthermore, Will knew things about very different topics: art, history, economics, law, chemistry, math, etc... which would be quite unrealistic, even for a genius. In fact, about Math, you actually need to practice that *beep* to be good, no one is just naturally figuring out theorems by casually reading about it.

And now... about psychology. I kind of laugh at Hollywood for making deep research about almost all topics, but psychology is always portrayed almost as "mystical". First of all, about the first "experts" that quit on Will... Most psychologist have experiences with different kinds of people, and it is not uncommon to find someone uncooperative or hostile. A psychologist quitting because a patient made a comment about his sexuality is just outrageous in my eyes. Finally, "attachment disorder" would not be in a file for someone Will's age, the term is not specific enough, they would have chosen a more appropriate personality disorder to describe him.