What is the prognosis? How likely is it that a person with schizophrenia will ever have a "normal" life?  

It Depends. Many folks with schizophrenia can and do live "normal" lives, especially and usually if they are compliant with their medication regimens. The prognosis can thus vary greatly, depending again, on the level of compliance with the medications. Some studies suggest that those with schizophrenia do best when treated with a long acting injectable form of an antipsychotic drug, like Invega sustenna (paliperidone palmitate)..
It can be good. If someone works with a psychiatrist, manages stress and takes medicines when needed a person can have a family, work regularly, and have those things we think of as "normal.".