Let's say I have a traded shiny nincada, level it up to 20, and get my ninjask, Will the Shedinja be shiny as well? And will the Shedinja have my OT or the OT of the original owner of the Nincada?
Good question, I am going to have to say yes. Shedinja has the same Nature, IVs, EVs, and moves as the Nincada that evolves so it will also be Shiny, and have the same OT. Source