Do the radioisotopes of Carbon 14 occur naturally or are they produced synthetically (man-made)?
The radioisotopes of Carbon 14 occur naturally. Carbon 14 is a radioactive isotope of carbon that has a nucleus containing six protons and also eight neutrons. You can read more about carbon at http://en.wikipedia.org/wiki/Carbon-14.
Both. As the wikipedia article indicates, some of the carbon-14 in the environment is from nuclear testing.