So you can say both 'lan se de yan jing' and 'lan yan jing'?
Yes, both are correct.
Why can't you say 她有藍色眼睛？
It's either 她有蓝眼睛 or 她有蓝色的眼睛
Yes, and you might think of it like this:
蓝眼睛 = blue eyes
蓝色的眼睛 = eyes of (the color) blue.
It's a mattet of habits. We either say 蓝眼睛 or 蓝色的眼睛
她眼睛是蓝色的 should be right, right? I wrote 她眼睛蓝色的
It will be "Her eyes are blue" instead of the answer