we do not share your data with anyone and there are many ways to control the visibility and storage life of your data here.
but the internet is a public space and you should always assume your data could be compromised.
be smart with your password, use tor or a vpn, and use pgp for sensitive communications.
Buy Bitcoin without verification - a September 2018 guide, not everything you've seen before has remained anonymous. Two options - either use a prepaid card and verify your phone and e-mail, or remain completely anonymous and use P2P exchanges.
Thanks Emeralds, people should keep in mind that even these exchanges have limits on unverified transactions. If they don't post them openly (eg wall of coins) then ask them before you buy. In general you will want to make multiple smaller transactions as you test an exchange.