Heritable doesn't necessarily imply genetic. Culture is heritable. Traits can propagate through generations memetically.

"Heritable" definitely means genetic when used in a technical rather than a casual sense, though. Studies control for environment by looking at, for example, identical twins adopted by different families.

Heritability refers to trait variation due to genetic variation within a population.

This is different than the amount genetics actually contributes to a trait.

While you are controlling for environmental factors in heritability studies you are still referring to a specific population. It can be the case that two identical genotypes across two different populations show two different phenotypes.

Isn't "~50% heritable" a different way of stating that the results are indistinguishable from a coin flip? That doesn't sound too hereditary.

No? Lets say we intro-/extroversion is either heritable (with prob .5) or random(with prob .5). If both of your parents are introverted you have a 50% chance of inheriting the introversion of your parents or a 50% chance at a coinflip, which gives us 75% for introversion and 25% for extraversion.

I'd rather interpret it as "50% are fixed (nature) and the other 50% are a coin flip (nurture).

No:

https://en.wikipedia.org/wiki/Heritability

No, because it's not a binary choice. There are degrees to which people are open to new experiences or extraverted.

I took it to mean a covariance of 0.5.