1520s, from L. fungus, learned alternative to mushroom. (Though funge was used in this sense late 14c.). The Latin word is believed to be cognate with (or derived from) Gk. sphongos, the Attic form...
Yes fungus can spread by just stepping somewhere that a person with toenail fungus stepped. If you do get toenail fungus, however, there are treatments that may eliminate it.