All of these are directly descended from Latin in exactly the same way that today's English is descended from 1900s English, just over a longer period.
Latin is certainly a dead language, even though it has living descendants.
The reasons for considering English circa 1000 and English circa 2020 to be "different stages of the same language" but Latin and French to be "different languages" are an arbitrary cultural distinction not rooted in science. The English of Beowulf is just as different from the modern variety as French is from Latin. And at every point from the introduction of Latin into France thousands of years ago until the present day, everybody could communicate perfectly easily with their own grandparents, and thought they were speaking the same language.
(Tangent -- certainly not all languages are descended from a hypothetical Proto-World, since we have examples of brand new languages forming: any creole languages, or Nicaraguan Sign Language. Whether most of the major language families are descended from a Proto-World is very much an open question, and probably one that will never be answered, since even if say, English and Navajo are genetically related, they diverged so long before we had written records that no trace remains.)
In any case, there's a meaningful difference between a language gradually changing over hundreds of years such that the newer varieties are quite different from the old ones, and a language truly dying, because it has exactly one remaining native speaker, and that person dies.
It's a question that linguists (who are scientists) strive to answer in ways that are useful to studying, reasoning about, and explaining language. It's not much different than the species problem in biology. Everyone knows that speciation happens gradually, but scientists still propose ways of defining and explaining speciation to aid in scientific inquiry. The labels and dividing lines themselves are not empirically observed, of course, but that doesn't mean they're unscientific or outside the purview of scientific inquiry.
I would be very surprised if such a thing exists.
Sure they are, although a debate wouldn't be contained in one paper written collaboratively by debating authors, as you seem to imagine -- it would play out over a series of papers, each of which cites previous papers and claims they're wrong.
For example, Timm 1989[1] argues that modern Breton is a VSO language, disputing the claims of Varin 1979[2], who claims it is SVO, which in turn disputes the traditional understanding that it is indeed VSO.
Or the famous paper of Haspelmath 2011[3] citing many other authors' proposed approaches to word segmentation and arguing that they're all wrong (i.e., that "word" is not a meaningfully defined concept in linguistics).
Where are the papers that you claim exist about the lines between languages? If this is really something mainstream linguists care about, you should be able to give examples in non-fringe journals.
I just checked the citations on the Wikipedia article for Middle English like you suggested, and found zero papers about whether Middle English should be considered "the same language" as modern English. Can you tell me which ones specifically you mean?
[1]: Timm, L. (1989). "Word Order in 20th Century Breton". Natural Language & Linguistic Theory, Vol. 7, No. 3, Special Celtic Issue, pp. 361-378 (https://sci-hub.tw/10.2307/4047723)
[2]: Varin, A. (1979). "VSO and SVO Order in Breton". Archivum Linguisticum 10, pp. 83-101
[3]: Haspelmath, M. (2011). The indeterminacy of word segmentation and the nature of morphology and syntax. Folia Linguistica, 45(1). (https://sci-hub.tw/https://doi.org/10.1515/flin.2011.002)
The weaker (and more reasonable) claim is that learning Latin improves your ability to recognize words and (very basic) structures in its descendants.
Anyway, my point is that it's an error to say that Latin "stopped changing". Other languages have changed similar amounts: modern Americans can't understand Beowulf, modern Greeks can't understand Homer, and modern Chinese people can't understand Confucious, but nobody would claim that English or Greek or Chinese died and stopped changing. The fact that people call Latin, but not English, a "dead language" is purely due to the fact that the different stages of English all happen to be called "English".
In an alternate world where Latin was exactly the same as it was in the past, and Italian is exactly the same as it is now, but Latin had never spread outside of Italy, I suspect that we would today call Latin "Old Italian" (or perhaps we would call Italian "Modern Latin"), and nobody would be having this discussion, despite the scientific/linguistic facts being identical to what they are in our reality.
I don't think this is the case: the language that Beowulf is written in is normally referred to as Old English. Chaucer is Middle English. Shakespeare is Early Modern English. William Makepeace Thackeray is Victorian English.
IMO, it's reasonable to assert that each of these are "dead" in some meaningful way: even Early Modern and Victorian English, despite their intelligibility, are simply not spoken by any group of current-day English speakers.
http://ancientgraffiti.org/about/ is an excellent resource specifically for Herculaneum and Pompeii, but it also links to broader collections to which the project has contributed.
There are interesting aspects of graffiti throughout the Roman Empire. Children (or exceptionally short adults) practised writing on walls; some taller people's graffiti showed not just literacy but familiarity with Virgil and even decent command of Greek and other second languages. Conversely, numerous graffiti are supporting evidence for partial Latin literacy among speakers of other languages, even among celtic-language informal epigraphers in the west and northwest in the first decades CE. It seems likely that these influences "accented" day-to-day Latin, perhaps comparably to https://en.wikipedia.org/wiki/Singlish .
A couple of centuries later and one could see a clear split between the classical register and early Vulgar Latin. Appendix Probi is interesting, and some examples are listed at https://en.wikipedia.org/wiki/Vulgar_Latin#Evidence_of_chang... which also draws some comparisons with Romance languages. (cf. https://en.wikipedia.org/wiki/Appendix_Probi )