why was the gate of ishtar anmed after the goddess ishtar?

Answer 1

I think that one is probably lost to history. Ishtar was one of the more powerful goddesses in the Mesopotamian pantheon, and it is likely she was seen as a protector against forces who would attack Babylon. But that's speculation.

Here is a cool picture of the Ishtar Gate (which is now at the Pergamon Museum in Berlin):
http://teachers.sduhsd.k12.ca.us/ltrupe/ART%20History%20Web/final/chap2NearEast/Ishtar%20Gate%20view%202.jpg