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.