How do stem cells produce 200 billion new blood cells every day? Does 1 stem cell division result in production of just 1 blood cell or many?
The hematopoietic stem cells are quite rare, and each progenitor cell produced by a stem cell gives rise to a large number of red blood cells (and other blood cell types).

I'm not sure if the precise number of offspring for the earliest progenitor cells is known in vivo, but recent cell culture models indicate that early progenitors can give rise to as many as 70,000 mature red cells. We also know that the erythrocyte burst-forming cell, a later stage cell in the erythroid lineage, gives rise to around 5,000 mature erythrocytes.

Red blood cells eject their nucleus in the final stages of maturation, and cannot divide thereafter. The ejected nucleus is consumed by a bone marrow macrophage, so it cannot be "reused" in any way. Hence, loss of the nucleus is probably not an advantage in terms of "production economy" --- a nucleus must be generated for each single red cell anyway.