How the Farplane works, is that the pyreflies that inhabit the Farplane will form something (all things are pryefly made, but in this case, the dead, as is the sole use of the Farplane) based on the memories/thoughts of other people. However, in the Farplane, only those who are dead will appear (assuming they did not become fiends in the process).

Simply put, the Fayth appear in the Farplane because they ARE dead. Yuna's memories of them made them appear. Tidus is the primary exception.

Luck does basically the same thing in each of the games where it was present (but not entirely). In this case, it determines your Critical Hit Rate, slightly enhances your Evasion, and slightly enhances your Accuracy. It is also said to help your Escape rate when using the manual commands.