The distinction between organic and inorganic carbon compounds, while useful in organizing the vast subject of chemistry... is somewhat arbitrary. Organic chemistry is the science concerned with all aspects of organic compounds. Organic synthesis is the methodology of their preparation.
No, it is not possible to contract the typical STDs, such as syphilis, gonorrhea, chlamydia, hepatitis B, etc. from wearing someone else's dirty underwear. However crabs and scabies, may be spread in this fashion.
Yes, if he has intercourse with her, he can get a penile (penis) yeast infection. A man who knows his sexual partner has a yeast infection should wear a condom to protect himself from getting a yeast infection. Men often show absolutely no signs of having a yeast infection if they do have one.