'Henny Penny', more commonly known in the United States as 'Chicken Little' and sometimes as 'Chicken Licken', is a European folk tale with a moral in the form of a cumulative tale about a chicken who believes that the world is coming to an end. The phrase "The sky is falling!" features prominently in the story, and has passed into the English language as a common idiom indicating a hysterical or mistaken belief that disaster is imminent. "Wikipedia"
The side plot revolves around Blanche trying to have her obituary retracted. The obituary falsely claims that Blanche was 68 when she died. In real life at the time, Rue McClanahan was 57.
Despite the fact that an improved vaccine for the measles was developed in 1968, vaccination practices did not effectively eradicate the virus in the United States until 2000 with contained outbreaks in the 2010s due to widespread and baseless claims about the vaccine's side effects.
Per the title, a chaser is a mild drink or beer taken after a shot of hard liquor.