ENGAGED. Caroline, 26, Princess of Monaco, elder daughter of the reigning Prince Rainier III; and Stefano Casiraghi, 23, playboy son of a wealthy Italian industrialist; in Monaco. The Dec. 29 wedding date was announced 15 months after Caroline's mother, Princess Grace, died following an auto accident on the Cote d'Azur, France. Caroline will be married for the second time, Casiraghi for the first.

MARRIED. Loretta Swit, 42, Nurse Hot Lips Houlihan on CBS's M*A*S*H series; and Actor Dennis Holahan, 41; she for the first time, he for the second; in Studio City, Calif.

HOSPITALIZED. Johnny Cash, 51, stone-faced country and western singer; to avoid chemical dependency; in the Betty Ford Center of Eisenhower Medical Center; in Rancho Mirage, Calif. Fearful that he might become hooked on drugs after taking prescribed painkillers for sciatic nerve spasms and surgery on a bleeding ulcer, the gravel-voiced Cash checked himself into a rehabilitation program.

HOSPITALIZED. Isaac Asimov, 63, sci-fi and nonfiction word factory, with 286 books to his credit and 14 more at his publishers; resting comfortably after triple-bypass heart surgery; in New York City.

AILING. Joan Miro, 90, protean Spanish painter of playful, dreamlike canvases; gravely ill with deteriorating respiratory disease; in Palma de Mallorca.

DIED. John Vivyan, 68, television actor who played the title role in the 1959-60 adventure series Mr. Lucky and more recently appeared in Simon & Simon and in WKRP in Cincinnati; of heart disease; in Santa Monica, Calif.

DIED. Rod Cameron, 73, swaggering cowboy actor; after a stroke; in Gainesville, Ga. Cameron played in more than 100 western and action films over almost four decades. On television, he played Police Officer Bart Grant in the series City Detective and later starred in State Trooper.

DIED. Fania Fenelon, 75, singer in the all-female inmate orchestra at the Auschwitz death camp, who recounted her ordeal in the memoir Playing for Time; of a heart attack; in Le Kremlin-Bicetre, France. Fenelon's 1976 book was made into a television movie four years later, with Vanessa Redgrave portraying Fenelon despite objections because of pro-Palestine Liberation Organization statements.