how much has ancient writing influenced modern day language?

In the sense that ancient writing was the modern at one point, greatly. Language changes depends on what is popular, and ancient writing can re-emerge into modern language but it's a complex dance. I would recommend the podcast a way with words to learn about language and its influences.

Quite a bit. Probably not a day goes by when you don't use, or at least hear, some catchphrase or cliche that was written thousands of years ago, in biblical books, or ancient Greek epics, or the speech of some Roman orator, or in the analects of Confucius.