Stars die because they run out of fuel to maintain a balance of the star's pressure and gravity, causing the star to die through cooling or a stellar explosion.
In the big bounce theory, the universe repeatedly expands and contracts into a new "big bang", seesawing back and forth in a massively big-picture timeline.
Likely not, with current technologies, the world as we know it would incur a mass extinction of most humans due to lowering temperatures, water bodies freezing, and gravitational instability.