Whew! Your questions are interesting ones, seizetheday, and to adequately answer them would take an essay several pages in length. But, lessee if I can give you a "TV Guide Synopsis" of my perspective:
Mental Illness has its feet in both the Nature and Nuture realms. For example, Erick Erickson's Developmental Stages strongly suggest that Nuture plays a big part in the outcome of the Personality. However, William White, in his book Born That Way, asserts that the personality is a genetically predisposed template; the personality is mostly Nature.
Just as other illnesses have a genetic predisposition, Mental Illness can be passed on through the genes. However, the reconfiguring of the brain's electro-chemical processes through organic means (e.g. drug abuse) can be a precipatating factor contributing to a Mental Illness.
Environmental Stressors (e.g. childhood abuse) can also contribute to the reconfiguring of the brain's electro-chemical processes, hence being another contributuing factor for Mental Illness.
Since certain neurotransmitters have been identified as being in levels greater or less in many Mentally Ill Individuals, this could also be a factor contributing to the type of behavior the Mentally Ill Individual manifests. For example, dopamine antagonists usually calms agitation. Hence, we can surmise that an over-production of dopamine in the brain causes agitated behaviors.
Mentally Ill Individuals are given a certain diagnosis because they manifest a group of symptoms. Diagnosis is a systematic approach, as the Professional utilizes the DSM-IV for symptoms and diagnostic criteria. That's the diagnostic process in a nutshell.
Of course Mental Illness spans the spectrum in its affect upon the Individual. Most Mentally Ill Individuals are quite capable of functioning adequately in the general community. Some Mentally Ill Individuals need constant Professional monitoring. The trend, in the last several years, is to allow the more severely Mentally Ill to live independently in the Community with regular visits by Mental Health Professionals.
Mentally Ill Individuals, as All Individuals, have Rights. There are guidelines, rules, and Watchdogs out there to assure everyone is theorectically treated fairly.
I don't believe I've addressed all of your questions, seizetheday, but this will give you an idea of where I'm coming from.
The best to you.