Is there a correlation between fine hair and higher densities in people with fine hair?

No not at all. Fine hair can have densities as much as coarse hair. However it does play a factor in the planning of the transplant. Go see a hair specialists to receive an in person evaluation.

There is no correlation with high density of hair and the caliber of the hair.  You would need high density of hair if you have a very fine caliber of hair to achieve the same look of fullness than those with coarse caliber of hair.

the thickness of the hair is independent of the density of the hair.  Get your donor density measured, a critical step in evaluating you as a surgical candidate, see below