Short answers, pulled from the story.
The Roman comic playwright Plautus coined the term tragicomoedia in Latin during the prologue to his play Amphitryon. He used the word somewhat facetiously when the character Mercury sensed the indecorum of including kings and gods alongside servants in a comedy.
Giovanni Battista Giraldi Cinthio developed a treatise on drama modeled on Roman comedies and tragedies in the mid-sixteenth century. He argued for a version of tragicomedy where a tragic story was told with a happy or comic ending, calling it tragedia a lieto fine.
John Fletcher stated that a tragi-comedie is not called so in respect of mirth and killing, but because it wants deaths yet brings some near enough to make it no comedy. Eugene Waith showed that Fletcher's tragicomedies also featured sudden revelations, outré plots, distant locales, and elaborate artificial rhetoric.
Friedrich Dürrenmatt described his play The Visit from 1956 as a tragicomedy. He suggested that tragicomedy was the inevitable genre for the twentieth century.
David Foster Wallace published Infinite Jest in 1996 as a notable example of metamodernist tragicomedy. Wallace writes of comedic elements found in living situations like halfway houses, which are places steeped in human tragedy and suffering.