Do we know how Greek dialects sounded?

No, we do not know what ancient Greek sounded like. We do know it did not exactly sound like standard modern Greek. There were several dialects in ancient Greek (Attic, which was a version of Ionic, Doric, Aeolic…) and certainly many local accents. In addition, pronunciation must have underwent some changes over time.

1. Do we know what Ancient Greek sounded like?
2. Can a modern Greek speakers understand Ancient Greek?
3. Did Ancient Greek have th sound?
4. Are Greek dialects mutually intelligible?

Do we know what Ancient Greek sounded like?

The pronunciation of Ancient Greek is not known from direct observation, but determined from other types of evidence.

Can a modern Greek speakers understand Ancient Greek?

Depending on the era and dialect, Ancient Greek might be totally incomprehensible even to a native Greek, like the Archaic Greek in the works of Homer, also called Homeric Greek, or somewhat comprehensible, like the Koine Greek of the New Testament.

Did Ancient Greek have th sound?

Like English (but unlike most languages), Greek had a TH sound. In Greek it was written with the letter theta (Θ θ). In English it is always spelled TH, just as you would imagine.

Are Greek dialects mutually intelligible?

Almost all of them are mutually intelligible with Standard Modern Greek, except perhaps for Tsakonian Greek. As with most languages, the dialect of Greek that you will hear depends on the region you are in.