No idea about childbirth stuff, but I can talk about child schizophrenia at length.
Pediatric schizophrenia is rare, and it sure as hell ain't pretty. Schizophrenia normally doesn't rear its ugly head until a person is in their early to mid-twenties. Schizophrenia affects maybe 1 in 100 adults; in a child of 6 or 7, we're talking one in millions. Some psychologists and psychiatrists aren't even convinced that kids that young can have full-fledged schizophrenia, and are incredibly reluctant to diagnose it.
Childhood schizophrenia isn't a subtle thing that a mother would "suspect" her offspring has. Schizophrenia itself is not a glamorous illness, and its pediatric version is a far nastier beast than the adult version. Most of these kids have symptoms that are far worse than what you'd ever see in adults. If they develop "negative" symptoms they're going to be very similar to kids with autism (in fact, many kids diagnosed with schizophrenia may be just mis-diagnosed autistics); poor verbal skills, poor social skills, arm-flapping, repetitive movements, listlessness, apathy, social withdrawal... in some cases, these kids don't speak at all. They have problems with cognition, and very little motivation to do much of anything.
The "positive" schizophrenia symptoms might actually be even worse. They have delusions and hallucinations that may be incredibly frightening, aggression, violent behaviour, incoherent speech, and long episodes of catatonia where they just stare off into space, refusing to move, speak or acknowledge anything going on around them. Most cases of schizophrenia have both positive and negative symptoms, but kids with predominantly positive symptoms are a nightmare to take care of. They have to be put on anti-psychotics, which shrinks their brains and can make their cognitive problems worse. They can be such a danger to themselves and others that they must be carefully supervised at all times. They can be unpredictable, and many of them feel as if they have no choice but to listen to what the voices tell them to. Many of them have sudden episodes of screaming, terror, violence or rage that make them hard to parent. On the whole, these kids don't do very well in the future - their rates of remission are far lower than adult schizophrenic, and roughly 10-15% of them end up killing themselves within 10 years of being diagnosed. Not pretty.
If you came to a doctor thinking your child was schizophrenic, they wouldn't just wave you off. You have to go through a thorough, six-month investigation where you consult with all kinds of mental health professionals, have your child do all kinds of tests and take detailed records of all your child's behaviour. It's an involved process - if you want to incorporate this disorder into your story, you'll need to do a lot of research.
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