How do you say “your beautiful" in Latin - the dead language

I want to be able to speak another language but don't know which would be best to try and learn. I'd rather not learn spanish but i will keep my options open to anything that is said.

i called a place where they teach different languages, i told them i want to learn japanese, russian and latin and i thinked of korean also, but they said there is no latin language.
how im supposed to tell them i want to learn latin language? should i tell them i want to learn latin-american or what?

Hundred years ago the most common language was Latin, Greek is even older than latin and was less popular, but it didn't die, Latin died and from it were born other languages. Greek evolved from ancient Greek. But HOW did Greek not disappear as Latin did?

Could you explain to me the process during history that made Greek be preserved through the years up now?

Thanks in advance