Besides the training (MD vs PhD) and money, what are the differences between neuropsychology and psychiatry?
They both seem to be concerned with the neurological basis of behavior.
I'd encourage you to take some time and read up on the forum, as they are very very different fields that lead to pretty divergent jobs. A psychiatrist is a physician who pursues further training in the area of psychiatry. A neuropsychologist is a psychologist (whether it be in Clinical or Counseling Psychology) who pursues further training in the area of neuropsychology.
The paths take about the same amount of time (~7-8yrs), but the starting salaries favor psychiatry...at least in regard to starting out in private practice. The top end of the spectrum for neuropsychology can make comparable amounts, but the middle 50% is far better for psychiatry. In academia the salaries are more comparable, but the vast majority of psychiatrists and neuropsychologists are not in academia.
1) Do they differ in their day-to-day practices/roles?
Any crossover in day-to-day practice is mostly incidental. Diagnosis of pathology can happen, but the vast majority of psychiatrists spend their time doing medication management, while neuropsychologists typically spend most of their time evaluating and diagnosing pathology.
2) How are their theoretical orientations different?
There are professional surveys that break down therapy orientation of psychiatrists and psychologists, so I'll defer to them.
3) Do they treat similar population and work in the similar environments?
The day to day work is so different, that this is hard to answer.
4) Would neuropsychologist be able to conduct researches that involve pharmaceutical drugs? or would that be a role for psychiatrists? (for example, effect of SSRI on certain behaviors)
Most psych-pharma is sponsored by pharma companies, so the typical path to securing this funding is much different than going after an NIH or similar grant. A neuropsychologist would have a much stronger background in research training (research methods, statistical analysis, grant writing, protocol development, etc), but those skills matter less when pharma companies are looking for a patsy.
(#4 is tongue-in-cheek, btw)