When a merit offers “…an additional Thaumaturgy/Necromancy path of your choice,” does that simply mean a character can learn the path? Does the character still need a teacher? Do you purchase the path at in-clan or out-of-clan costs?

Yes, the character can learn the path without a teacher. The costs are listed in the merit’s description. For example, Necromantic Expertise and Thaumaturgic Expertise allow a character to learn an additional path of blood magic at in-clan costs.