Short answers, pulled from the story.
The Sumerian spelling dEN-KI usually translates to Lord of the Earth, yet this definition does not fit all known functions of the god. Some researchers argue that the second element ki(g) might mean favor or benevolence instead of earth.
The name Ea first occurs in personal names from the Old Akkadian period around 2300 BCE. Earlier translations interpreting Ea as House of Water are now regarded as implausible by most experts.
The sky god An is named as the father of Enki in multiple sources including the myth Enki and the World order. The creator goddess Nammu was regarded as the mother of Enki in the tradition of Eridu.
His main cult center was the city of Eridu which was regarded as his home already in the sources of the Early Dynastic Period. The temple of Enki in Eridu was named the E-Abzû meaning House of the Abzû.
Enki devises a plan to create mankind from the clay of the Abzû in collaboration with his mother Ninmah. In another myth called Enūma Eliš, Ea fashions mankind from Qingu's blood after he is executed.
The worship of Ea was introduced into Anatolia through Hurrian cults possibly as early as the third millennium BCE. His name was rendered as Eyan in Hurrian and Aaš in Hittite while Iyas appears in Luwian texts.