Wow this is a big question.
How to handle the reading would have a lot to do with how well you knew this person. People with mental illnesses are so much more complex than that one label. Remember while reading for them that they are an individual, not a disease.
Also it would matter how well their symptoms were under control and how severe in general their disease is and how well they have learned to cope with their illness.
I have read for quite a few people with psychiatric disabilities and other mental challenges, as well as people in recovery programs for trauma and substance abuse. I find it easier to read for the ones I know. They are just people with challenges, and the more I am aware of what those challenges are, the more I am able to choose my words wisely.
Avoid shaming and blaming in any way. Don't accuse. Many people with mental illnesses were abused as children, even if no one has identified that into their label. "you are bad" or "you did something bad" can set off a bit of a post trauma response that both you and them might not understand, but it can bring on feelings of shame, anger, defensiveness that are over the top for what is happening in the present.
I don't ever use a spread that has positions that are solid fortune telling, in a situation like this even when pressed to. I don't read about other people for them and insist the reading stay entirely focused on themself. Some of them have issues of paranoia that make this unsafe and confusing for them. So I stay in the present and focus just on the sitter NOW. It's better even not to poke into the past too much. I modify spreads.
I'm very careful in my deck choices. I won't use a deck that contains any images that are sarcastic. Beware of cards like a miser 4 of pentacles.
The whole pentacles suit is likely to be about safety and belonging issues rather than money with some of these people. Read pentacles cards widely and study base chakra and earth element materials, so you can learn to do this.
I have never gotten into a power play in a situation like this :-0 I cannot expand on what re-pete-a is saying. But then my reading style is pretty laid back and exploratory, and flexible. There is nothing to challenge.
Good luck and most of all have fun