If some woman with a std wears under wear all day, takes them off , then someone else puts them on without washin them, will that second woman catch it?

Most likely not : Std such as gonorrhea, syphilis, chlamydia is transmitted sexually most of the times, but in theory, if someone has an active herpes lesion and the underwear is in contact with the lesion and somene else with some sort of genital cut wear this underwear immidiately thereafter, there is a possibility of acquiring herpes that way.