1. Yes I'll give you that one, if the range of emotions displayed in a family is extreme enough to incorporate physical beatings etc it is entirely possible that a child would develop schizophrenia. I don't believe that blurred concepts of good and evil etc would actually cause this sort of behaviour, but if we argue that it did, then schizophrenia is a possible (but by no means inevitable) outcome. Perhaps, I am being too optimistic in regards to the strength of the human mind, but I don't think the majority of people would be completely ground down by such situations to the point where schizophrenia was triggered.
2. I don't think this is an understatement, manic depression can be just as serious (if not more) than schizophrenia. The reason I suggested manic depression over schizophrenia is simply because manic depression seems the more likely outcome of an emotionally extreme background than schizophrenia. Schizophrenia afterall would require fairly severe hallucinations (typically auditory AND visual in England) to qualify, which would seem like too severe an emotional reaction to a broken home in my eyes.
3. People can develop all kinds of fragments of neurotic disorders from their backgrounds, as well as some traits of psychotic disorders. This soup of fragments of disorders doesn't qualify a person as "psychotic" or "neurotic" but it does serve to create a very disturbed and eccentric individual. I would expect a person with a background like the one you suggested to be highly unpredictable and unstable in their emotions (perhaps even going as far as to be diagnosed manic depressive) but for the most part I think people would overcome the worst effects of such an upbringing.
At the end of the day, a person's reaction to psychological trauma depends greatly upon what they are like as an individual. Some people would probably become psychotic in the world you suggested, others would benefit from it. "Mass schizophrenia" however, sounds very unlikely to me regardless of the situation.