Short answers, pulled from the story.
The Roman comic playwright Plautus coined the Latin term tragicomoedia in the prologue to his play Amphitryon. He used it somewhat facetiously, through the character Mercury, to justify mixing kings, gods, and a slave in the same play.
John Fletcher defined tragicomedy in the printed edition of The Faithful Shepherdess (1608), writing that it "wants deaths, which is enough to make it no tragedy, yet brings some neere it, which is inough to make it no comedie." His definition focuses on whether or not characters die.
Giovanni Battista Guarini's Il Pastor Fido, published in 1590, provoked a fierce critical debate about genre mixing. Guarini's defense of the form succeeded, and his model of modulated action, stylized characters, and a pastoral setting became the standard for continental tragicomedy for more than a century.
Samuel Beckett, Tom Stoppard, John Arden, Alan Ayckbourn, and Harold Pinter are among the post-World War II British playwrights who worked in the tragicomic genre. The Swiss dramatist Friedrich Durrenmatt also wrote tragicomedies, describing his 1956 play The Visit as one.
Landgartha (1640) by Henry Burnell holds that distinction. Burnell explicitly described it as a tragicomedy, but critical reaction was universally hostile, partly because the ending was neither happy nor unhappy.
David Foster Wallace's Infinite Jest, published in 1996, is described as a notable example of metamodernist tragicomedy. Wallace drew on the comedic aspects of life in a halfway house set against a backdrop of human tragedy and suffering.