I'm pretty sure that you can already do all of this. I can't currently find the option to entirely de-list from search, but I thought I had it on before.
My full name exists less than a dozen times on Facebook in all of Germany, and the name does not occur anywhere in the world outside of northern Germany.
This is quite an issue.
Name plus city plus one other piece of data (approximate birth date, school(s) attended, former employer(s), a few other associates/contacts, profession) are very often enough to uniquely identify an individual, even with an otherwise common identity.
Yes, but you can set all of those to private and thus effectively delist yourself from Facebook Search. The only thing that really has to be public nowadays is your name.