1. How to stay anonymous when you buy and sell Bitcoin?
Use Decentralized exchanges (e.g. Bisq, hodl hodl)
2. How to anonymize Bitcoin if you purchased it from a centralized exchange?
As long as you not submit any KYC to an exchanges, you're fine. But if you already submitted, use a mixer and don't withdrawing all the funds in one times since it make you could be traced easily.
Besides this, I would like to find out what is the best anonymous bitcoin wallet for 2021. Please share your top privacy-protecting bitcoin wallets and highlight the reasons they this or that wallet in your top.
Both Wasabi and Samourai wallet are the good option for privacy since they have CoinJoin features.