Short answers, pulled from the story.
Vulgar Latin refers to the range of informal, spoken registers of Latin used from the Late Roman Republic onward, as distinct from the formal literary language of Classical Latin. Scholars now generally consider them to form a continuum rather than two separate languages, with speech evolving faster than the written form and the written language exerting pressure back on speech.
The early 19th-century French linguist Francois-Just-Marie Raynouard is often regarded as the father of modern Romance philology and is credited with developing the theory. He argued that the Romance languages shared a common spoken ancestor distinct from Classical Latin, which he called la langue romane.
Linguists draw on Roman grammarians' notes about informal usage, recurring errors in stone inscriptions and curse tablets, private letters and business documents such as papyri from Egypt and writing tablets from Hadrian's Wall, veterinary and agricultural manuals, early Christian texts, and loanwords borrowed into neighboring languages like Basque and Welsh. The comparative analysis of modern Romance languages is also used to reconstruct features of spoken Latin.
Regional differences begin to proliferate clearly in Latin documents from the 7th century CE onward, roughly coinciding with the rise of the first Arab caliphate and the end of Roman dominance over the Mediterranean. Statistical analysis of earlier texts does reveal some regional variation by around the 5th century CE, particularly in the handling of certain vowels and consonants.
The definite article in most Romance languages developed from the Latin demonstrative pronoun ille, meaning "that". Writers like Gregory of Tours in the 6th century and the author of the 7th-century Chronicle of Fredegar show ille being used in ways that function more like a definite article than a true demonstrative. Romanian placed the resulting article after the noun rather than before it, yielding forms like lupul for "the wolf" from lupum illum.
The original synthetic Latin future tense was replaced in Vulgar Latin by a construction combining the infinitive of a verb with a conjugated form of habere, meaning "to have". The phrase amare habeo, literally "to love I have", contracted into the future tense endings found in French, Spanish, Portuguese, and Italian. The first known written attestation of this new future appears in the 7th-century Chronicle of Fredegar.