Not sure why you didn't check the links yourself before you responded to their email or before you removed the posts.
That said, it is not a violation to simply post links to material protected by copyright.
Depends. If you're linking to music or warez then you are almost certainly going to get into trouble. Linking to pages that contain copyrighted text or images, there's probably a lot more leeway.
Note that even if it was a recording the poster had made themselves, unless they also WROTE the song themselves it could still be a copyright violation. I would simply write back and make the best case you can, and forget about the idea that it's a "strike" against you. I'm not aware of any evidence that Google thinks in those terms.