Another example: Quechua, the lingua Franca of the Incan empire, is still widely spoken on its past territory, even though the empire ceased to exist 500 years ago and the conquerors brought with them a very different language and civilization (Spanish/Christianity).

The cultural switch brought about by the Spanish conquest succeeded fully on the coast, but not so much in the mountains.

Yep. Latin was the lingua franca (or at least one of the major ones) in Europe until 1800 or so, more than 1000 years after the fall of the western Roman Empire.

Maybe you are confusing what lingua franca means. Yes the literature used Latin but at that period only a tiny fraction of people could read or write. There where many more languages that we even have today spoken by the general populace.

French maybe came close to being a Lingua Franca in the 18-19th century when almost all aristocracy could speak, read and write it but then again the people did not. The Real Lingua Franca was a mix of Italian, French, Spanish and Greek that was used by the merchants of the Mediterranean. Only English has the People Mass to be considered a Lingua Franca for all intents and purposes.

Spanish, too.

Was Latin really the lingua franca, or just the language of liturgy, over that period?

Latin was also the lingua franca of nobles and merchants. Lingua Franca Mediterrania itself, the language spoken by medieval sailors in Italy, Egypt, and nearly all the coastline of Mediterranean is a creole of Italian, Portuguese, and Arabic. To the point that Shakespearean Moors spoke it as "Arabic".

Then, the language of science until the 1900s is Latin. Isaac Newton wrote in Latin. Nearly all scientific papers and books were published in "Neolatin".

Latin was also the language of academia, which gradually separated from the Church starting in the Late Middle Ages.

Both. (Less and less towards the end, of course).

Well, it's sticky, but not sticky enough that it's known as the "lingua angli". It will probably outlive QWERTY, but I'm not so sure about the calendar, and it'll die long before base 10.