Do They Know What Latin Sounded Like in Roman Times?

Latin was still spoken in the Roman Catholic Church up until the 1970 's so I'm sure there are still priest who can speak it. Latin is not considered a dead language.

Church Latin is pronounced very differently than what I was taught in Latin class in high school 60 years ago. We often look at poetry in older versions of English to find clues about pronunciation. I should imagine this has been done with Latin as well, but don't really know.

The best we can go by for the layman would be to speak with a Catholic Church elder, or the one who knows the most who can tell you about the changes of the centuries, but I think it would be very similar to what they would here in Rome, we in other countries would have our own cultural tones

It is now classed as a dead language because it is no longer spoken as normal conversation, the closest you will get is Italian and to a linguist even that isn't close

Chetak

Latin scholars are divided,and there have long been disputes over what the actual pronunciation used by the Romans was.

Vulgar Latin - a more informal version of the language - began to be used by Roman writers from the mid 3rd century,and Catholic clergy using latin today are using that rather than Classical latin.

So,no one really knows for sure.

No, we don't. There was once a movement for "New pronunciation" in Latin, which was supposed to go back to the way it was pronounced a couple of thousand years ago; but whether this was anything more than wishful thinking I don't know.

Under the "new" system, for example, Julius Caesar was pronounced Ee-Oolius Key-zar.

It would be impossible to know exactly what type of accents the ancient Romans had- there were likely regional and class variations. For example, the provincial "vulgar" Latin dialects would have been different from the Latin spoken by educated elite people in Rome. People still speak Latin today, but nobody speaks it as a first language, and most likely speak it with accents of their native languages.