I don't think they were hysterectomies but Dr Cotton is based on an actual doctor who ran an asylum. He believed that insanity stemmed from untreated infections in the body so he'd remove organs. When he died in 1933 he was praised by The New York Times and other publications. And i think that those were Bureau agents, i think they were gonna take Nuck in for tax evasion. Might be a little reference to what happened to the real Nucky down the line.