1. You didn't provide any source for this (and I can't find anything online to back it up; granted I only searched for a few minutes). Facebook isn't listed in their portfolio, for example: http://www.carlyle.com/Portfolio/Alphabetically/item8774.htm.... And I couldn't find any mention of the Carlyle Group in the Facebook S-1 filing, either. You could be right, but I'd like to see the evidence.
2. The Carlyle Group is a huge private equity firm that owns all or part of hundreds of companies around the world. Suggesting (without any evidence) that they own these companies as some shadowy method to share private data across them is ridiculous. Your edit makes it even more clear that you're more interested in some kind of conspiracy theory than the obvious truth, which is that the Carlyle Group either didn't invest in Facebook or did so because they thought they'd make good money. And if they invested early, like you say, then they were right.
Thanks for the reply. I'll try to look up connections, but for right now it seems to be impossible with Google SERPs including Facebook mentions of Carlyles the world over. That is, search for anything "facebook" on Google and you'll get a million FB pages due to the word "Facebook" in every page title.
EDIT: Looks like the Google News Alert has reached Carlyle Headquarters. Expect silent downvotes.