It's likely they will ask you KYC verification and write all transaction details. If government decide to track you, you'll be tracked easily.
Those exchanges use KYC only when using important amount.
Thats correct but the use of exchange site as anonymity is concern is never a good one because almost all crypto currency use Google ReCAPTCHA which i believe can still be used to collect users data.
1) use BTC mixer such as WASABI
But there are talks about people getting involved in illegal things just because their BTC were mixed with illegal related BTC.
Wasabi is Bitcoin wallet with built-in CoinJoin, not mixer.
That's correct but it a wallet with confidential payment technology which can also be consider was a means of making anonymous payment and shouldn't be consider as mixer but it still good than some mixing company i dont want to mention name.
It better to make use of a mixing company though when anonymity is big priority.