Currently my bitcoin is store in Exchange.
Storing your coins on an exchange can be risky for a great number of reasons. There is a saying amongst bitcoiners: not your keys, not your coins.
I wonder if I should simply generate bitcoin address and private key in BitAddress and send to this address and safely store the keys that was generated.
It is ...
Use a Bitcoin wallet: https://bitcoiner.guide/wallet/
If interested to trade using a DEX so you always got the keys for your bitcoin: https://bisq.network/
For Ethereum related questions: https://ethereum.stackexchange.com