Is there a way to contact a member privately, like on Facebook; or to contact by email?
I suggest spending some time looking at the available Help pages, found under the Help link at the top of the page. These will give you an idea of how this site is intended to work and how it (and all the other related SE sites) are different from social media sites.
One key point to keep in mind is that this site is part of a much larger network of Q&A sites, and many of the norms, features, and functions are based on network-wide experience and discussion. There is a special meta site for questions/requests that apply to the whole network, and if you go there you'll find multiple requests for a way to contact other users - but they've all been rejected.