What is the origin of "pratfall?"
Merriam-Webster (whose definitions you cite in your question) dates the term pratfall to 1930. However, a Google Books search finds an example that is a bit earlier. From Lee Wilson Dodd, The Great Enlightenment: A Satire in Verse, with Other Selected Verses (1928) [text not visible in snippet view, but visible here from what is supposedly a 1927 source]:
Once timid in dim corners, like the mouse,
Professors now, like actors, "count the house,"
"Take stage," demand a "spot," inspire a "clack,"
And, to "get laughs," will sit upon a tack,
Or do a "prat fall" with the veriest clown
To gain th' attention of our Planet-Town.
Another early spelling of the term is with two t's—but it retains the same meaning. From Roger Whately, Jack O'Donnell & Henry Hanemann, The Silver Streak (1935):
PRATTFALL — Violent posterior gravitation.
According to Harold Wentworth & Stuart Flexner, Dictionary of American Slang, first edition (1960), pratt or prat is only slightly older than pratfall:
prat [or] pratt n. The human posterior. 1923: "Pratt." Hecht & MacArthur, Front Page, III. 1946: "He does not fall on his prat." Time, Mar. 11, 63/1. Very old. v.t. To move behind someone in order to observe him without being seen or to get into a position to rob him. Underworld use.
prat fall [or] pratfall A fall on the backside or rump; said of a person. Often used esp. of falls taken by clowns in comedy routines. Wide theater use. 1939: "A perfect pratfall. ..." Edmund Wilson, New Republic, Apr. 26, 332. ...
Robert Chapman & Barbara Kipfer, Dictionary of American Slang, third edition (1995) essential repeat Wentworth & Flexner's entry for pratfall, but they put a number to the age of prat, where Wentworth & Flexner had made do with "Very old":
prat or pratt n by 1567 The buttocks; = ASS ... {origin unknown}
J.S. Farmer & W.E. Henley, Slang and Its Analogues, volume 5 (1902) provides a brief excerpt of its early usage in The Merry Wives of Windsor (1596):
Mrs. Page. Come, Mother Prat; ...
Ford. I'll prat her {Beating him}.
Over the early centuries of its use, however, according to Farmer & Henley, the term prat (like the word buttock) was more often used in plural form than in singular, as in Richard Brome's Jovial Crew:
Fiddle, Patrico, and let me sing. First set me down here on both my prats.
Since the 1928 instance of prat fall already places the term in the context of clowning behavior, it seems not at all likely that the word originated in vaudeville or earlier theatrical lingo. But I have not been able to find an explanation of why Elizabethans settled on prat as argot for buttocks.