Based on the information provided above, I carefully draw the following inferences and express some feelings I have analyzed.
First of all, your father seems to be a suspicious, weak, introverted, unsociable, confident and hesitant person, and his position in the family seems to be on the edge. Your mother's ability is in sharp contrast to his various performances. As you described, your mother is respected, but her father is in a weak position. She has lived in a female-dominated family environment for a long time, and your father may have been suppressing himself. As an adult male, his performance in life is often inconsistent with his true inner thoughts and emotions. When faced with the conflict between self-esteem and inferiority, he can't solve the problem smoothly. In this emotional experience for a long time, people's way of thinking may be distorted. All the above are enough to have a bad influence on his heart, which may aggravate his inferiority complex. He experiences self-blame all day, but he can't do anything about it, which may easily lead to psychological imbalance and some disorder in his behavior.
For example, your father went home to complain after working at your uncle's. Let's think about it, is it possible that your father doesn't work well there, but because of his personality or face, your father blames himself for being excluded, which is a way to avoid others blaming him for his personal reasons. On the other hand, what your father said about being victimized and bullied can be interpreted differently according to the specific situation. If your father was really treated unfairly when he was working with his uncle, and his description of his father after he came home is based on facts, he may have been excluded, but it is normal to exaggerate his feelings and situation when describing it. However, it is also possible that your father's complaint is just his delusion and has no factual basis, so you have to suspect that there may be some mental problems.
For your mother's illness, the burden of the family seemed to fall on him as a father at that time, and he could feel the great responsibility, but at the same time he also knew his own ability, the loss of porridge money (although it seems to us to be a trivial matter, it happens from time to time in daily life, but it may not be a trivial matter for your father, and he may blame himself for this trivial matter), and all kinds of worries, pressures and depression may all lead to psychology.
Of course, the two cases I analyzed above are only based on the information I have, so to judge whether your father really suffers from the delusion of being murdered, more and more detailed information is needed, such as his childhood experience, personality characteristics, daily life status, interpersonal relationship, physical condition (because we don't rule out that organic diseases may cause these problems), major events and so on.
Due to objective reasons, I can only make some superficial analysis and assumptions, which may be slightly biased in some places, and I don't know if I can help you, but I sincerely hope that your problem can be solved as soon as possible, and I wish you a happy life!