As a never-signed up non-member of the FB empire, how do I find out what they know about me without them finding out even more?
Answer: you can't. Neither can FB users. I just tried "download your data" with a friend who uses FB. FB's record of your browsing history, and their advertising profile for you, are NOT included. The closest thing I found is the list of advertisers who've targeted you by (basically) uploading a contact list with your name/email/whatever in it, which they probably obtained from sources other than FB.
What you want is a US GDPR that effectively outlaws the consumer surveillance, direct marketing, public records, people search, and 'instant background check' industries.