From what I recall, you need a year of biology, a year of general chemistry, a year of organic chemistry, a year of physics, and a year of calculus for most medical schools. You do not need anatomy, nor neuroscience, unless the requirements have changed in the last 10 years, which I doubt. There are a few ways to look at the question of whether to take anatomy as an undergrad - it'll make anatomy easier when you are in medical school as it'll be familiar, but it also prevents you from taking a different class while you are in college that you won't have an opportunity to take in medical school. A neuroscience class could mean anything as far as I can tell - as a psychology major, a lot of the classes probably fit into the neuroscience category.

Your question about research is a little unclear - I have heard that medical schools like to see that you've done some research as an undergrad, although I don't know how much it really matters.

A PhD program is something completely separate from medical school. You probably would want to do some research to make sure it is something you really enjoy doing and understand what is involved before deciding to get a PhD. I would say it is not necessary to do a lot of research, but some research would definitely be a good idea for a PhD program. Actually, I don't know if research experience matters much for clinical psychology programs - I would guess it's more important for research PhD programs.