She has wide eyes to me describes a physical characteristic of her face. It is not really natural. She has wide-set eyes ( a physical condition where the eyes are farther apart than normal)
She is wide-eyed - describes an expression in her face - she is surprised or astonished.
1. I'm not quite as tired as I was last week. Is the quite meaning "completely" here? No, it means that I am a little bit less tired now than I was last week.
2. It's not nearly as cold as yesterday. Does this mean: It is not so cold as yesterday. Yes. It also implies that yesterday was really cold.