What Are Crash's Ties to Dr. Cortex?
Crash was an experiment by Cortex, attempting to make a super soldier out of him. The plan ultimately failed, and Crash now works for the side of good.
Who is Coco?
Coco is Crash's sister, but she does not make an appearance until this this game. She was mentioned in Crash Bandicoot.
Why Are the Crystals so Important?
They contain the energy needed to either stop or start the planets from aligning. Aligning the planets would cause a solar flux that would destroy many things.
Is Dr. Brio Evil?
That depends on your interpretation. Brio destroyed Dr. Cortex's space station. Their relationship was rocky in Crash Bandicoot 1 and 2, and Brio had no intentions on harming Crash.
Are there Secret Levels Throughout each Stage?
Yes. Crash can play the secret levels by stepping on or touching platforms with a question mark.