what exactly does increasing/decreasing population growth say about the country? also, if birth and death rates remain the same, what is the population pyramid going to look like in a couple of decades?

It depends on who is dying. If infants are dying, it quite different than if older adults are dying. In wars, or genocides, the deaths skew the population pyramid. I remember visiting N Ireland in the 60's...many young men were dying then, and there were lots of young women looking for potential husbands. So who is dying is critical to your question.