The sky3ds card is compatible with 3DS firmware 9.6 and can run unlimited 3DS games, although it does not natively support homebrew applications without using the ninjhax exploit. To run homebrew on a 3DS with firmware 9.6, users can opt for an R4 card, which supports homebrew apps at a lower cost. The document provides detailed instructions on how to activate ninjhax using the cubic ninja game and also discusses the limitations of homebrew and emulators when using the sky3ds card.