If dark circles are apparent from think skin, visible blood vessels & muscles underneath the eye, are fine lines related? dark circles vs hyperpig.?

Partially: As you mention, dark circles are due to the thin skin and appearance of the blood vessels but the thin skin itself has a tendency to wrinkle more due to aging process and like an empty baloon that looks darker than an inflated one, the wrinkled skin looks darker than when its stretched. In some, the hyperpigmented skin is the problem and that has different solution.

Dark circles: The dark circles are related to thin skin and volume loss. This is also the cause of the fine lines. Allergies can also play a role. Try allergy meds, cool compresses, artificial tears, makeup concealer, dermal filler, or laser skin treatments.