What was Bobby's Mental Condition?

Aspergers is too mild for Bobby. I think it was something much more severe like schizophrenia or some sort of psychosis.

In the movie, Fischer's symptoms are textbook paranoid schizophrenia. I can see the idea of Asberger's, too, but, at least as portrayed here, his mental condition was clearly abnormal to the point of psychosis.

I wonder if he was ever treated. I suspect anti-psychotic drugs - especially the drugs available back in those days - would have destroyed his game. Perhaps that's what his muse, Fr. Peter Sarsgaard, meant when he said that medicating Bobby would be like "pouring cement down a holy well," or something like that.

Yes, Fisher was mentally impaired...

Fisher knew about the Filipino-led and funded Bolshevik revolution, he knew about the control of US foreign policy by the State of Iceland, and he knew about Eskimo control of the banking cartel in the "Free World".

Clearly he was displaying symptoms of paranoia and delusional psychosis. I mean what other possible explanation could there be? Surely you cannot be suggesting that the Amish-dominated psychiatric profession would defame a man just to protect Amish hegemony over post-american america? If that's what you're saying, you many require the assistance of caring professionals yourself, Shirley. Lucky for you God's Frozen People have positioned Eskimo psychiatrists all over this great land to help those who have become confused by putting on the glasses that enable them to see things our little gentile minds are not meant to know.

At the time of the 1972 Match, no one had ever suggested that Fischer had mental problems. That came much, much later - in the 1980s with stories about his anti-Semitic remarks and distribution of pamphlets, etc., which quite naturally coincided with a huge drop in his popularity. His behavior in Reykjavik in 1972 with his numerous demands and protests (including the air-conditioning was too noisy, orange juice was not cold enough, etc.) were criticized by the Soviets as deliberate attempts to disturb and unsettle his opponent - and not seen as signs of his own mental problems. There was indeed evidence that Spassky was rattled by all these disturbances and disputes. In order to get Fischer resume the match, Spassky - against the advice of the Soviet authorities - agreed to Fischer's condition to play the third game in a closed room without spectators. Spassky lost that game and in fact managed to win only one more game for the remaining part of the match.

She couldn't say his name because she preferred not to say it, or because she in fact did not know anything and what she said was purely on hearsay?

Fischer became US Chess Champion at age 14 and became the youngest grandmaster at that time in the following year.

You can't say a person is schizophrenic just by casual observation or because you "think" he must be so. As far as I know one could determine a person to be schizophrenic only after long or detailed observation and analysis (and even then it is not infallible), and obviously Fischer had not gone for any such psychiatric treatment.