Maybe, but subject to both points: firstly, a person must have sufficient information to know the symptoms of certain mental illnesses. At present, information on any of them is easy to find, so it would be sufficient if a person was interested in the issue and studied materials on this topic. I'm surprised why no one said about this: to know the disease, you must at least know its symptoms.
Suppose that we are dealing with a polymath (after all, people with higher education, in including medical ones, they are prone to mental illness no less than everyone else). Here the question of the safety of critical thinking is already included, in this case - to determine the known symptoms in oneself.
In my subjective opinion, if both conditions are met, it would be most difficult for doctors from the field of psychology / psychotherapy / psychiatry: it is a very severe emotional stress - to move from the category of doctors to the category of patients in this, also stigmatized, by the way, the region (this despite the fact that even many doctors today tend to stigmatize it). It is very possible that self-diagnosis will fail due to banal negativism. But this is questionable - a subjective view of that and a subjective view.
Lack of criticality to one's state, one's actions, judgments, to one's personality in neuropsychology is called anosognosia and can be included in the symptom complex of some mental disorders associated with a disorder of the bioelectrical and / or biochemical activity of the brain or with diffuse / local organic lesions of the central nervous system and, in particular, the brain. Anosognosia can differ in type and severity: from underestimating violations and lack of anxiety in connection with a defect, to unawareness and denial of the disease. If we talk about the spectrum of diagnoses, in which there is often no criticism of their own state, it includes in itself such disorders as: organic lesions of the frontal lobes of GM (the so-called "frontal syndrome"), progressive paralysis, senile dementia, sometimes - with schizophrenia (the main productive symptoms of schizophrenia are delusions and hallucinations, perceived by a person as really existing), also in bipolar affective disorder, etc. In these disorders, criticality is one of the main criteria for the mental state of patients. Of course, there are also mental disorders in which criticality is completely or satisfactorily preserved: with various types of depression, for example.
Actually, the answer to the question: self-diagnosis is difficult, both because the context of a particular mental illness, and due to insufficient competence for making a diagnosis, it is better to entrust this matter to a specialist.
Depends on the mental illness, whether the criticism of your condition is preserved. If yes, then usually the illness weighs on the person, he realizes that something is wrong with him. But it often happens that a person being in a psychiatric hospital thinks that he is now at a ski resort or visiting relatives. Don't get carried away with self-diagnostics :)
Of course it can. Studying many patients at the Department of Psychiatry, taking into account the fact that everyone in that clinic was lying voluntarily, almost everyone understood that they were sick. Not everyone understood exactly their form of the disorder, but, for example, one patient knew that if he drank alone at home, it would be difficult for him to restrain himself so as not to attempt suicide, and the other could no longer constantly see the faces of people in his window in the evenings , although he lived on the 7th floor. So many of them understand. Another thing is, when a person has developed meningitis or has experienced a severe stroke, then we simply cannot find out what the patient understands and what does not.