Follow up question, if I may: why is Latin considered a dead language when it has been spoken continuously by the church? Was my Latin teacher wrong? Or are there differing opinions?

There's been a couple threads on this. The short answer is yes, the would probably have understood each other OK.

My field is early French and the transition from late Vulgar Latin (i.e. the spoken/non-Classical language) but there may be some points of interest I can offer.

For one thing, all our records are of course of written language which differs a great deal from speech. We cannot be sure how much the examples we have even of Vulgar Latin necessarily represent the spoken language.

This is form Rickard's classic history of French:

There are a great many texts in Vulgar Latin, from all over the Empire, and they suggest an almost suspiciously homogenous language which, while it diverges in a great many ways from Classical Latin, seems to have firm rules of its own and to rise, artificially of course, above such regional variations as may have already existed. Most students of Vulgar Latin, however, are reluctanct to believe that there was any substantial regional differentiation before approximately the sixth century A.D.

Of course when the Empire collapsed the regional variations and assorted language change gave birth to the modern Romance languages. It is generally considered that the structures of Empire sustained the 'suspicious' homogeneity mentioned above.

But none of this tells us much about mutual intelligibility because setting aside grammatical and lexical variation, accent counts for a huge amount. Many Americans struggle to understand my Briish accent even when I use structures and words they themselves might produce!

Even today there are a variety of Latin accents. Ecclesiastical Latin is mainly pronounced like modern Italian (eg with a palatalised 'C' in incipio) whereas British public school pronunciation (you find both old and 'reformed') is quite different (eg a /k/ in incipio). Little changes mount up to mutual confusion and so it is highly likely accent alone would hinder efficient communication (at least to start).

You would also need to consider the degree of education of your Roman because modern Latin is based on the classical, literary language which is really rather different to what the man on the street spoke. Imagine a foreigner with a working knowledge of C S Lewis's style going to a Yorkshire pub and trying to keep up.

In other words difficulties are going to emerge not just from how the language has changed over time.

I think I have implicitly answered your second question: Latin changed enormously since the fall of the Empire (evolving into Spanish and Italian and Romanian etc) but 'modern Latin' harks back to the golden, classical age.

Well you should ask a linguist. But I can tell that Latin as it's taught in Italy resents from Italian phonetic reading, so an Italian who speaks Latin with an ecclesiastical pronunce would say "Certum" with a soft c while an ancient Latin would say "Kertum" with and hard c.

Follow up question: I am studying history in the first semester. A professor said, that latin had no dialects (unlike greek for example). Why is that so?

This might be removed, but I figured I'd offer my input. Sorry if this isn't up to standards.

I'm in my fifth year of Latin. Primarily we learn to read and write but some teachers like to focus more on pronounciation. As you have said, Latin evolved, and would not always be spoken the same way even within the same time period. What we consider "church" latin pronounces the "c" as a "ch" or a "soft" c, whereas in classical Latin a c would always be a "hard" c. Classical Latin also prounounces the v with a w sound, whereas "church" Latin pronounced it the way we do. So, theoretically, it depends on whether the modern speaker is educated in vulgar/church Latin or classical Ciceronean Latin.

However, it probably wouldn't matter. You would be able to understand someone who pronounces some English constructions a slightly different way. So the answer is yes, they most likely would be able to understand each other.

Slightly related question: when I've asked my teachers how we know specifically certain differences of classical vs. vulgar Latin, they claim there are Roman comedies that make fun of the way the country-folk spoke Latin. Is there any truth to this?

That depends on what you mean by a modern speaker of latin. Some of the church latin can be very different to silver age latin. But a 1st C roman and someone who speaks church Latin would certainly be able to understand each other in the same way that swedes can understand norwegians (don't quote me on that analogy though, but you get the idea). However, most academics, I think, learn golden age Latin (Cicero, Julius Caesar, Ovid etc) which was 1st century BC, so understanding someone off the 1st C AD (silver age Latin) would have its difficulties, such as some vocab differences, but it's probably as different as English was 100 years ago so they could easily communicate. That is assuming that any non religious scholars actually speak Latin not just study and translate it, which of course they don't

I would point out that English has actually been a living language for the past 1500 years, where as Latin has not