Short answers, pulled from the story.
The Eleusinian Mysteries began as a Bronze Age agrarian cult centered at the Panhellenic Sanctuary of Eleusis in ancient Greece. Archaeological evidence suggests these rites were derived from religious practices of the Mycenean period, predating the Greek Dark Ages.
The Greater Mysteries lasted ten days from late summer around September or October during the month of Boedromion. Sacred objects traveled to Athens on the 14th of Boedromion while priests declared the start of rites on the 15th and initiates entered the Telesterion on the 19th.
Six categories of priests served including Hierophantes whose office was inherited within the Phileidae or Eumolpidae families. Only requirements for membership were freedom from blood guilt meaning never having committed murder and not being a barbarian unable to speak Greek.
Initiates consumed barley mixed with pennyroyal which has inspired speculation about psychotropic effects from ergot fungus growing on barley. Fragments appeared within dental calculus of a twenty-five-year-old man offering evidence of consumption at the Mas Castellar site in Girona Spain.
Closing happened in 392 AD reported by Eunapius historian biographer Greek philosophers. Julian reigned from 361 to 363 attempting restoration of mysteries becoming last emperor initiated into them.