Conan is not Thoth Amon's apprentice. By any stretch of the imagination.
In Howard's work he deals with stuff having to do with the sorcerer priest only twice. The God in the Bowl, where he's hired to steal a bowl that has Thoth Amon's sigil imprinted on it, and The Phoenix Sword, where Thoth Amon works with Ascalante to try and overthrow Conan, King of Aquilonia. They never meet in either story.
Derleth and other writers wind up expanding his interactions with the sorcerer by making them nemeses.
As to Conan's ethnicity, he is a Cimmerian, roughly analogous to Irish or Scottish. His skin has a ruddy tone because he's in the sun all the time and has a tan. He's not a Pict or a Native American.