Can you tell how fertile a woman is by the appearance of the private parts?

Not at all: No. The things that make a woman fertile are her ovaries, her hormones, the uterus and fallopian tubes. All of those are either tested by blood work or by imaging inside.

Depends: Although you cannot tell how fertile a woman is by looking at her, you can often see during a cvervical exam that she is at her "most" fertile as the mucous increases in amount and stretchiness.