He did play "in secret" and in not so secret. Just not FIDE events. See Polgar.

Muhammad Ali did quit training for a long time. In fact he was stripped of his title and both his physical appearance and lack of sharpness were evident when he came back. The man who lost to Frazier the first time was not near the man who flattened Cleveland Williams.

We don't know why Fischer refused terms at least not precisely why. Speculation stated as fact is worthless. His requests were not that extreme as compared to previous champions, but he was denied those requests.

As mentioned before, Fischer had physiological problems stemming from his childhood, his mother and the fact his father (Hans-Gerhardt Fischer) was not his father, instead his father was statistician Peter Nemenyi.