If I have a Shiny Nincada, and I evolve it with an extra spot in my party, what happens? Do I get a Shiny Ninjask and Shiny Shedinja, or just a Shiny Ninjask with a normal Shedinja?
Yes. The way that a Pokemon's "shininess" is determined is based on three values: The Original Trainer's ID, their secret ID, and the individual Pokemon's personality value. Given that Shedinja retains the original Nincada's personality value, a shiny Nincada will produce a shiny Ninjask and a shiny Shedinja upon evolution.
Side note, the exact formula used to calculate shininess is:
(TrainerID xor SecretID) xor (PersonalityValue31..16 xor PersonalityValue15..0)
PersonalityValue15..0 represent the highest and lowest 16 bits of the 32-bit personality value respectively.