IF A BABY IS BORN IN GREECE, WILL IT AUTOMATICALLY BECOME A GREEK CITIZEN?

No, it will not. The concept that a baby born in a country will automatically become a citizen is quite common on the American continent. In Europe no country has the so called birthright citizenship. In Greece a newborn baby will receive the status of its parents. If the parents are asylum seekers, the baby will be included in the asylum application of the parents, after presenting the baby and the birth certificate to the Asylum Office. If the parents are already granted an asylum status, the baby will receive the same status like them.