No. The Adopted Trait refers to the racial traits in the same section as the Adopted Trait, like Warrior of Old. Otherwise it would to powerful for a trait.
NO. <rolls eyes> Race traits are different from Racial traits. Do a search. Many threads on this same question. Adoption gives you access to a RACE trait not a RACIAL trait.
(Eye roll was in paizo's direction for choosing the similar names not to the question...)