How to tell a diagnosis from an actual state? Since diagnoses merely represent what a doctor is thinking, how can a mental patient know the difference between de facto "reality" and what decisions a doctor is planning?

We know planning is not real but a mental patient can't say that a decision from a doctor is not reality, even though a decision from a doctor is not anything that has a physical existence.

So if the doctor decides a 5150 or likewise, I'm not asking about the legal processes but how you could convince that a diagnosis is not just a model. 

What is a mutual indicator for every sz or psychosis? IF there is no common indicator, how can it be a diagnosis or a condition? What is absolutely impossible with e.g. schizophrenia that is possible with no schizophrenia?

Since paranoid schizophrenia could be just a person who is worried, which doesn't exclude anything does it.
Doctors are trained not to diagnose a patient subjectively, but to use objective criteria. Psychologists and psychiatrists worldwide have agreed on a set of criteria, by which each doctor should arrive at the same diagnosis, if faced with the same patient.

The current practice is that all mental disorders are defined by a list of symptoms. If a patient shows a certain minimum number of symptoms from this list (no matter, which), it is assumed that he is very probably suffering from that disorder. A sample can be found under the section "Criteria" in the Wikipedia article on Schizophrenia.

This is the currenty way to diagnose a mental disorder, because, despite all its weaknesses (see the section "Criticsm" in the DSM Wikipedia article for an overview), it is believed to be the best of all bad methods (akin to Churchill on democracy) and no replacement has yet been found (unless you count Antipsychiatry as helpful in dealing with mental problems).

The lists of criteria and the minimum number of symptoms are given in the Diagnostic and Statistical Manual of Mental Disorders (currently DSM-IV-TR) and the International Statistical Classification of Diseases and Related Health Problems (currently ICD-10).

As you can conclude from this, a mental disorder is not a reality. It is a construct that consists of a collection of possible symptoms. The "actual state", as you call it, the physiological reality, is not accessible to the psychologist or psychiatrist.