1) Should you assume that because someone has a mental illness they are in any significant measure more likely to commit crimes or unethical actions? No, no you shouldn't. Almost all mentally ill people and non-neurotypical people can tell right from wrong quite well and exercise impulse control. From an ethical standpoint, it is also important to know that people with mental illness are more often the victims of crimes than the perpetrators.

2) But... what should we do when someone harms others in unconventional ways, without any obvious motive or gain from doing so? Perhaps I jumped to conclusions to suggest it was mental illness, but I think in these cases it should definitely be investigated as a possible cause during trial. Just because the care you need to rehabilitate a person who is suffering from a significant and specific mental disorder might be different from how you rehabilitate someone without the same condition. Even if she is found both guilty (she could distinguish right from wrong at the time and thus not legally "insane") but mentally ill, it should be taken into account so that she receives the right type of care if/while imprisoned.

We use "mentally ill" to describe people who are unable to participate in society in a sustainable and positive way. We don't have a perfect way to decide whether someone even is mentally ill, but it usually involves an inability to behave the way the patient, the patient's family, or society itself (in the case of crime) would like.

That could include someone with OCD who loses a lot of time to washing her hands, but it also includes people who harm others for pleasure.

Until we have different words for those categories, people with illnesses like depression are going to be under the same incredibly general umbrella as people who poison others.