Do synthesists get the eidolon's natural attacks? They get the "special abilites", does this include natural attacks? All I can find is this link, but even this lacks clarity:
natural abilities.
Yes, but not directly.
All natural attacks an eidolon possesses are part of its evolutions. (Even the ones it has due to its base form, like claws or bite, are specified as free evolutions.) As such, you gain the ability to use any natural attacks your eidolon could.