If a prion is just misfolded proteins, is it dead or alive? Does it have "life" encoded inside it?

Metaphysically. Prions reproduce themselves by inducing the normally folded prion protein to misfold. I would not think this is 'life' but it is open to interpretation.
Prion. Prions are proteins that have changed conformation, so that the normal function of the protein inside the cells won't work. The prions' also causes other normal proteins to misfold and make more prions, spreading the process. The prions affect many cells in the body, but they particularly harm nerve cells in the brain, causing progressive rapid degeneration. They are not alive, and have no dna.