Does self replicating RNA occur in nature?
They probably existed in the beginning of life (on Earth or somewhere else). But any free RNA now would be almost immediately devoured by bacteria or other organisms.

Bacteria are ubiquitous. That's one of the first things you learn in a microbiology course. We do this experiment a few times: open up a Petri dish far from a Bunsen burner, and in a few days you can see how many bacteria and/or fungus colonies have grown in the Agar. Any good microbiology book will show you this. I have none right now with me, but have just found a few links by  searching for "bacteria are ubiquitous" on Google: Understanding Bacteria, The Purple Phototrophic Bacteria, Bacteria in Agrobiology: Plant Probiotics and Public Health and Infectious Diseases. 

As for the science studying the origin of life, I recommend The Fifth Miracle: The Search for the Origin and Meaning of Life, by Paul Davies.