What are some fun, open questions relating to blackbody radiation? (Research paper ideas needed)?

That's got nothing to do with black body radiation. The most interesting thing about it was that it was the first clue about quantum physics - WHY does black body radiation depend only on temperature, and why is there a peak in it? Classical physics has no answer - look up the "ultraviolet catastrophe".

Mars radiation has nothing to do with blackbody radiation, but rather charged particles coming from the sun and cosmic rays from deep space. An interesting subject, however, is how closely the cosmic microwave background matches a blackbody radiation curve; so closely in fact that when they graph the curve the error factor is typically much thinner than the line tracing the curve when printed.