Are there any guidelines about preachers who use psychiatric words about people?
If a person goes to a meeting thinking it is a Bible study but then finds the teachers using psychological words and doing some kind of therapy, is there any law protecting them against the teachers claiming to know psychology and claiming to have identified illness in others?
That would depend on how you behaved at the meeting.
All people running a class have a duty of care to the other participants if one person is showing signs of mental illness.
It's tricky - it depends a lot on the laws in your jurisdiction and the interpretation of words like "psychotherapy", "mental health treatment" and so on, plus how strictly these laws are enforced. In my jurisdiction they are only just now beginning to regulate psychotherapy and it's still unclear what exactly regulation will look like.
If you are in an area with no regulation, then probably in a strictly technical legal sense there is nothing to stop a Bible study teacher from doing some sort of psychotherapy. That doesn't make it OK. I'd say it's a major red flag. A responsible pastor would discreetly suggest that someone look into seeing a qualified mental health professional, not make on-the-fly diagnoses in the middle of class.
I suggest doing some research on what's allowed in your area. If you think your pastor is a basically decent person but doesn't quite realize what they are doing, perhaps have a quiet word with them about it. Their reaction will tell you a lot about the sort of person you are dealing with.
A degree in religious counseling (they exist in the states) would allow a "preacher" to do as such, but this would be spelled out before seeking advice. And when you go to theology for therapy, remember that the theology comes first.
"Remember that theology comes first." This definitely applies to any spiritual teacher or psychologist who uses A Course In Miracles (ACIM) as the basis for their "therapy/counseling." Look further for info on ACIM as well as Endeavor Academy (EA) and Unity Church. EA now has "counselors" posing as "spiritual teachers" , psychics, hypnotherapists, and life coaches" advertising on the internet. They have "infiltrated" society and have a close knit group of professionals who will attack you legally and other wise if you say anything negative about them. This is really scarey stuff.