It seems that you just found out about the little pot of gold that you hold and you may see a bit "lost" in what should you be doing and how to deal with this news.

First of all congratulations. 20 BTC, at it's current price, can chance the life of everyone and you should not let this excitement translate into fear / stress.

how to sell anonymously for cash? Most exchanges will ask for some sort of ID since the government demands it (at least I know that Kraken and Binance do this), at least for high amounts of trading. May I ask the need to sell anonymously? Do you have some sort of fear that people may found out who you are or something like that?
how to exchange for stablecoins anonymously and safe?Stablecoins, from the limited knowledge that I have, may be frozen with no notice. Please think twice before going this path.
how to store stablecoins? - See previous answer

Whatever you do don't go all in with the 20 BTC. My suggestion would be to pick an exchange, try to exchange a small amount of BTC and see how it goes.

Whatever you do, just take it easy. If you have BTC in a cold storage no one can take them from you, assuming you don't fall for those scams that try to trick you.