I turned on my tablet after downloading a Linkin Park album off of the Play Store. I turned it on and an app says "Get Free Music Download" and I feel like it's very harmful. Any advice?

Which app sent you that message? It's probably not going to harm your tablet, but it may be trying to redirect you to a site that will encourage you to spend money on purchasing more music.

Out of curosity, which Linkin Park album did you download?