Were the inmates of the mental institution actually ill (psychologically?)

No they weren't because they showed signs of reasoning, physical involvement, democracy.

They showed signs of reasoning when nurse ratchet took away
That guys cigarettes and he was giving perfect reasons to as why he should get them back and she was not corresponding appropriately. When she did, her reasoning was it was because they were gambling...but, in an asylum should there be gambling? Wouldn't that mean that the patients are smart enough to play cards which requires metal stability? Or to place bets accordingly? Which would require decision making?

They showed democracy when McMurphy asked to put the TV on and ratchet said no, they all decided to have a vote which shows that they understand and can think of ways around their obstacles in their life (in this case being ratchet) and having a sense of

They showed physical involvement and body control by playing basketball with guards and that played with a high degree of pace. This shows that they have body control and they can think on the spot. Generally a mentally unstable person to the degree of being put into an asylum must need care, medication, and monitoring daily.

How does McMurphy help the inmates?

McMurphy helps the inmates by giving them some sort of hope and self confidence. He teaches them how to work together and be a unit. He plays basketball with them and shows them how to work as a team. He gets got through to chief when nobody else could and showed chief that there's a better world out there and that's why Chief broke out in the end, because McMurphy gave him that confidence. McMurphy brought life into the institution and he helped the inmates gain self confidence because near the beginning when the nurses did the group meetings no one would speak up but later on in the movie, one of the patients (. ) asked for his cigarettes and demanded that he get them right away and also made valid statements as to why he should get them back and also when ratchet told him to keep calm he calmed down right away, this shows that he gained self control and self confidence which he never had before Murphy arrived.

What behavior modification techniques do nurse ratchet and the other staff use to make McMurphy conform to the rules?

Behavior modifications that nurse ratchet and other staff members use is the electric shock, they also use medicated abuse. For example when McMurphy choked nurse ratchet they shocked him 2 xs as much, gave him paralyzing medication and took out part of his brain. Also when McMurphy caused that fight to break out at one of the meetings he was zapped with the electricity and that's also another example.

Can the asylum be seen as a