1. I think it's probably a variation of the phrase "take on a life of its own," which means "to become very large, important, or hard to control" as defined by Merriam-Webster. In this context, it probably means that the video went viral, meaning the view counts multiplied exponentially like a virus.
2. Afterlife means life after death (which is a bit of an oxymoron). It's used figuratively here, so it doesn't have to do with anybody's death. It would depend on the context, but my guess is that the video became irrelevant (the video's "death") but then somehow regained its popularity.