The biggest thing, as you said, is figuring out what is happening in your world. What factors are killing people and what factors are keeping them alive. Assuming a pre-birth control world there will likely be more births than we see in the modern western world, but with less health care and food, new births are less likely to survive past infancy. With war and such, there are plenty of opportunities for people to die later on.
I think so, for the purposes of fantasy games, people need to consider different factors related to race. Many of the fantasy races have much longer life spans than humans, yet typically lower populations. I think the general assumption is the other races have lower birth rates.