I've been sent those packets offering to become a Nielsen family, and looked through the included description of how it works.
1) Nielsen does explicitly target children, insofar as Nielsen families are supposed to give them data on the usage habits of every member of the family, including the kids. That said, the decision of whether or not to become a Nielsen family remains firmly in the hands of the heads of the family. Perhaps regardless of the consent of its younger members.
2) They do also now track participating families' Internet usage at large, like Facebook's app was doing. I don't know whether it relied on a VPN or some other technology.
3) I think that most people could understand the TV consumption tracking that used to be Nielsen's bread and butter. But, at least based on the recruitment materials that were sent to me, I didn't have a clear understanding of the extent or nature of Internet usage data collection. I assume the story would be similar for most other users, especially minors.
Based on that, I think that a lot of these comparisons are comparing what Facebook is doing now to what Nielsen was doing 20 or 30 years ago. Which is fair comparison to explore, but let's be careful not to absolve the Nielsen of today from any scrutiny in the process.