It's impossible to be completely anonymous or to buy btc completely for free... Do not trust this kind of websites.
You can remain anonymous by never using centralized exchanges and using only decentralized exchanges. Using TOR and quality VPNs that don't keep logs. Never fill out any KYCs, mix your bitcoin to cover your tracks and don't reuse addresses. Anonymity is possible but it's not easy and not everyone can follow all the rules of the game.