Re: FaceBook part of the question. Here is an excerpt from an article explaining that your wife did NOT necessarily do anything on FB but did perhaps search interracial on the Internet somewhere:
Some ads you see on Facebook are posted using this Exchange platform. Let's use a scenario to understand this:
You are planning to buy a new laptop. You go on Apple's website and sift through their catalog. The website would place a cookie on your device. Advertisers can just specify on Facebook Exchange that users with a cookie from Apple's website be shown an ad from Apple.
So, when you log into Facebook, you would be shown an ad from Apple. It does not matter that you were logged out of Facebook when you visited Apple's website. The ad will be shown based on your browsing habits outside of Facebook. In a sense, Facebook might not even know that you visited Apple's website, as the ads are created using your data (using tracking cookies) compiled by the advertisers. In addition, you might see the same ad on other websites, too (not just on Facebook), as the same advertisers engage with different ad exchanges.
Although, from my experience to join a PRIVATE group usually someone must submit your name (perhaps her new friend).
Now as to why she might 'want' to belong to one of these private groups, I will speak from personal experience. I belong to one private group of Swinger friends and I did belong to a BDSM/Swinger combined group. Both were more out of curiosity, I thought it would be sexy and fun,both were at the beginning but eventually they became like any other FB group of friends (blah blah blah) LOL
I hope you two have a wonderful date night going over her fabulous week and what might be ahead for both of you.
ENJOY