Why do we die?Because if we didn't, the world would become unsustainable and we would die from other factors.
Why do we age?Telomeres. Instead of explaining what's going on with that, I'm going to give you a link to browse at your leisure. But as a quick and dirty: DNA replicates from the '5 to '3 prime direction. Because of this, some of this telomere is lost during replication. As replication continues, the telomere will eventually cease to exist and the cell will under go apoptosis (self induced suicide). As this continues to happen we will eventually lose our somatic cells and be unable to repair damages to our bodies. From that, we appear ragged and will eventually die.
http://www.news-medical.net/health/Telomere-What-are-Telomeres.aspxWhat is aging of cells, and why does it happen?See above.
Why dont we live in a moment where cells have evolved to not age anymore?There are cells that do not age. They are called cancer cells.
Why didnt the cells have yet evolved to immortality?Cancer cells.
Why?They regenerate their telomere using an enzyme called telomerase.
http://www.nature.com/news/2010/101128/full/news.2010.635.htmlWho says in the future our cells will not evolve to a point of regenerating themselves and we never age?No one can "say" either or, but immortal cells are a huge problem.
Why do we grow? Why dont we just stay babies? (evolution I know) So why didnt we evolve enough to reach immortality?We grow from our bodies switching genes on and off, stimulating growth of various parts of our bodies. If we didn't grow, then we would not have a very sporting chance at reproduction.
Again, immortality is bad and goes against the established biological function of life.
Why do we live in this moment of evolution and not another?Um... Because you were born into this time and not another time?
The factors for this question are limitless, so you can't really answer it justly.