Thank you for providing a great amount of detail with your question. The more information provided, the better able I am to answer your questions.
An “easy” way to think about the situation is this: if you had two children and one was destructive, dangerous and a threat to the other, doesn’t the innocent child have the right to be protected? The answer is yes. You would have no choice but to do whatever was necessary to protect the innocent and vulnerable child from the potentially dangerous child. Think of yourself as the innocent and vulnerable child. You have to protect yourself. It is not selfish to want to protect yourself. No one else is going to do it. It is necessary and it is simply an act of self-preservation.
It is also important to view this situation from the proper perspective which is that your boyfriend is mentally ill. “Normal” relationship standards no longer apply. He may be capable of having a healthy relationship in the future but at this time he can’t. I understand that you love him and don’t want to leave him but love cannot cure schizophrenia. Only treatment can and at this time he is not willing. This is the reality of the situation.
At this point in time, I believe that your boyfriend has the potential to be dangerous. There are multiple reasons why this may be true. One is that he’s constantly accusing you of having an affair. If he truly believes that you are betraying him, then he may become upset and want to retaliate. Other major “red flags” include the fact that he won’t take medication, he’s actively psychotic, he refuses all treatments, both his behavior and mood are unpredictable, he has a history of violence and abuse toward you, he shows no remorse for that abuse and he claims that he has murdered individuals in the past. He is very unstable and unpredictable. This puts you in danger. Individuals with schizophrenia are typically not dangerous but under certain circumstances they can be. In addition, when individuals with schizophrenia are violent the violence tends to be directed toward their family members. You are at risk.
To answer your specific questions, can you convince someone with schizophrenia that they have the illness and that they need to be in treatment? In approximately half of the cases, individuals with schizophrenia recognize that they have the illness and they need to be in treatment. The remaining 50 percent do not recognize they have a mental illness and will not engage in treatment due to a condition called anosognosia. Individuals who lack insight into their illness have a worse prognosis than individuals who have insight. Here’s a link to a previous answer I provided to a similar question that further discusses anosognosia.
Individuals who do not recognize their illness have the potential to eventually accept treatment but in many cases this does not occur. You may benefit from contacting the National Alliance for Mental Illness (NAMI). Many of the members have years of experience dealing with the exact issues you’re facing. They are a great source of information, support and practical advice.
You asked whether mood swings are common among individuals with schizophrenia and if so how long do they normally last? Mood swings can occur with schizophrenia and in particular schizoaffective disorder (a variant of schizophrenia) but they are more common among individuals with bipolar disorder. How long they last depends on whether the individual adheres to treatment. With the proper treatment, mood swings can be decreased or eliminated. Without treatment, they may continue unabated.
Your final question is: Can he ever live without treatment? The research shows that the majority of people with schizophrenia require some form of treatment in order to stabilize. Studies consistently show that individuals who do not adhere to treatment have more psychotic relapses and generally never fully stabilize. Treatment is the best way to prevent future relapses.
I understand that ending your relationship may be one of the most difficult choices you will ever have to make. Try to help him in any way you can but when you’ve exhausted all options you must stop before it becomes a detriment to your life. I would never advocate ending a relationship with someone who is mentally ill simply because they are mentally ill but you can’t abandon your life to save someone who may not be capable of being saved. The choice that you are facing is one of the ultimate tragedies often associated with schizophrenia. Schizophrenia has led to the breakdown of many families and relationships. Greg Bottoms in the book Angelhead: My Brother’s Descent into Madness powerfully explains the pain that the illness has brought upon him and his family.
On the bright side, with treatment there is hope for even the worst-case scenarios. I have witnessed firsthand the remarkable difference treatment can make in the lives of people with schizophrenia and their families. It can be transformational and inspirational. Treatment can save lives.
I would recommend that you enlist a therapist or another mental health professional with expertise in schizophrenia to assist you with this complex problem. If you have any additional questions, please feel free to write again. I will do my best to answer your questions or to recommend organizations or other resources that may be of assistance to you. I wish you the best. Please take care.