Sometimes population declines, like after the plague in Europe, can improve the lot of survivors by freeing up resources and increasing the returns for labor. But the reverse -- that population growth makes things worse -- doesn't necessarily follow. It depends on a lot of other factors, and in most of the world, including most of the third world, lower death rates and improved living standards have gone hand-in-hand.
I think so - the basic idea being people have less kids. That's because having more kids is an insurance policy for a high death rate.
(a) Health is an end in itself. (b) Tackling non-letal diseases that keep people from working, will raise living standards.