A closed system refers to something where nothing comes in or goes out. The earth, on the other hand, is always gaining energy from the sun - hence, the earth is an open system. Again, life on earth is subject to an open system. It gets energy from the sun. In the far, far, future, however, we can predict that life on earth will cease to exist because the sun will engulf the earth.
Natural selection is perfectly capable of design.
It didn't happen by chance. By the way both genetic mutations and natural selection have both been observed in the lab and in nature. Yes, many times. Experiments have been done with fruit flies where one species of fruit fly is broken up into two populations and after a period of time the two populations are re-introduced and unable to reproduce together. Most mutations are NOT good things.