Finding life on Mars might have major implication for Mars colonization. Preservation of this life from contamination from Earth is an open problem. On the other hand, humanity may be an active force in the dissemination of life in the solar system and beyond. Humanity might eventually create Exobiology.
Water, free oxygen and chlorophyll are all possible tracers for life on other planets that could be detected by astronomers.
If extra-terrestrial life is ever found, it will follow the laws of evolution. However, It will be interesting to know if the evolutionary paths followed are similar; with DNA, similar proteins and amino acids or if differents ones are used by different life forms. About 500 naturally occurring amino acids are known, but only 20 appear in the genetic code of life on Earth. So there is a wide variety to choose from, and we don't know if the selection on Earth was random or optimised in some way be evolution.
The Search for Extra-Terrestrial Intelligence (SETI) is usually done by scanning the sky for any radio (or other) transmission that would indicate an advanced civilization. So far no such transmissions have been found. There have also been searches for signs of large artificial constructs such as Dyson spheres and for traces left be high velocity starships.