Meaning and usage of "dead-and-alive"
The OED has an entry for dead-alive with a variant form dead-and-alive.
It's in "frequency band 2", which encompasses rare terms unknown to most people. (Although you didn't notice it, Merriam-Webster also gives both variants, saying "less commonly, dead-and-alive". It also says "Popularity: bottom 10% of words".)
The OED's definition is:
Dead while yet alive; alive, but without animation; dull, inactive, spiritless.
No etymology is given, although in the entry for "dead" it relates it to other similar combinations such as "dead and gone", "dead and buried", "dead and done".
The first citation for "dead-alive" in from 1617:
1617 S. Collins Epphata to F. T. 453 The Monke that liues in pleasure, and delicacie, and idlenesse, is dead aliue.
By the end of the 19th century it is being applied to locations:
1868 ‘Holme Lee’ *Basil Godfrey *xxvi. 138 This..dreary..dead-alive place.
Neither the OED nor M-W mention that either of the variants is BrE or AmE. I don't believe the terms are commonly used in either variety.
Here is the entry for dead alive (and dead and alive) in Jonathon Green, Slang Dictionary (2008):
dead alive n. see MAN ALIVE ["the number five"] n. dead alive adj. (also dead and alive) 1 {mid-19C} stupid, dull. 2 {mid-19C+} miserable, down in the mouth.
Eric Partridge, A Dictionary of Slang and Unconventional English, second edition 1938) has a somewhat longer entry for the term:
dead alive, dead and alive. (Of persons) dull, mopish, cf. deadly lively, q.v.: C 16–20: S[tandard] E[nglish] till mid-C. 19, then increasingly coll[oquial].—2. Hence of things, esp. places: dull, with few amusements, little excitement ('a dead-and-alive hole'): coll[oquial]; from ca. 1850; now S[tandard] E[nglish].
Partridge's entry for deadly lively reads as follows:
deadly-lively, adj. and adv. Alternately—or combining the—dull (or depressing) and the lively; with forced joviality; esp. to no purpose : coll[oquial]: 1823, 'John Bee'.
The Bee reference is to John Bee, [John Badcock], Slang: A Dictionary of the Turf, the Ring,the Chase,the Pit, of Bon-Ton, and the Varieties of Life (1823), which offers this entry for deadly-lively:
Deadly lively—is one who is half stupid, but pretending to his wonted activity and nous.
Nous, here, probably refers not to the French pronoun for "we" but to the Greek noun for "mind, perception, or sense" (ηους).
John Hotten, A Dictionary of Modern Slang, Cant, And, Vulgar Words (1860) has this very brief entry for dead-alive:
DEAD ALIVE, stupid, dull.
And finally, from John Farmer & William Henley, Slang and Its Analogues Past and Present, volume 2 (1891), we have this:
DEAD-ALIVE or DEAD-AND-ALIVE, adj. (colloquial). — Dull; stupid; mopish; formerly deadly-lively. [Cited instances:] 1884. H.D. Traill, in Eng. Ill. Mag. I. 541. The city has greatly revived of late ... it has ceased to belong to the category of the DEAD-ALIVE, and has entered that of the lively.
You can read Traill's sentence in context in "Two Centuries of Bath," in The English Illustrated Magazine (June 1884).
So we have dictionary entries for dead alive, dead and alive, and deadly lively before the end of the nineteenth century, with definitions signifying an unflattering idea of dullness with regard to either a person or a place. I should emphasize that most of these sources focus on British English slang.
The most exhaustive resource for American slang that I have access to, J.E. Lighter, Random House Historical Dictionary of American Slang (1994) does not mention dead alive, dead and alive, or deadly lively at all. Presumably, people in the United States, having access at need to dead from the neck up felt no need to plunder British slang for an alternative. Like other U.S. natives who have checked in on this question, I've never heard "dead and alive" used in a slang sense.