Is it possible for organic molecules to form in an oxygen-free atmosphere?
Yes, it is perfectly possible for organic molecules to form under a wide variety of conditions, including in an oxygen-free atmosphere. There is a good article here: http://www.astrobio.net/news/modules.php?op=modload&name=News&file=article&sid=14 about the organic chemistry currently going on in the oxygen-free atmosphere of Saturn’s moon Titan.
The short answer is “yes”, and in fact one does not need atmosphere at all. The definition of organic is simply that the molecule must include both at least one carbon and one hydrogen atom; and hydrocarbons (that is, organic molecules) have been been detected on the surfaces and the surroundings of comets as well as in the drifting dust clouds of the interstellar medium. See for instance: http://parseval.club.fr/CV/Articles/Article7.pdf –a paper about organics detected in space around comets, or http://www.astrochem.org/science.html –a site about Ames Laboratory’s researches into various types of organic molecules, including amino acids, in a variety of places,or http://www.pnas.org/cgi/content/full/98/5/2138 –a paper analysing amino acids found in meteorites.
Yes, as long as you define atmosphere as the gaseous envelope of a celestial body. If you mean an oxygen-free environment, then, I’m not so sure. Oxygen paired up with a couple Hydrogen (H2O) is a different story. “The ‘Miller Experiments’ were able to achieve spontaneous growth of organic monomers in an evironment similar to those conditions on Earth “… shortly after Earth first accreted from the primordial solar nebula.” Stanley Miller was a graduate student in biochemistry. He built an apparatus and filled it with -water (H2O -methane (CH4) -ammonia (NH3) and -hydrogen (H2) -but no oxygen” He hypothesized that this mixture resembled the atmosphere of the early earth. (Some are not so sure.) The mixture was kept circulating by continuously boiling and then condensing the water. The gases passed through a chamber containing two electrodes with a spark passing between them. At the end of a week, Miller used paper chromatography to show that the flask now contained several amino acids