Billions of years from now, the sun will blow up or do something drastic that will kill all life on Earth. I wonder if people will still be around when that happens, or if we will have become extinct before then. In any case, people should still be around when our children and their children and their children's children and many more generations are born!

That depends on what you mean by "blow up". The sun is held together by its gravity, or else it would fly apart, because it basically is exploding continuously and has been for billions of years. Eventually the sun will release much of its mass, and that probably will destroy all life on Earth, though (if the sun doesn't cook the Earth first, that is).