Does blockchain.info keeps my private key(s) in their wallets of database? I am referring to the wallets on their website.
What other private information do they use?
When I registered on blockchain.info they have provided me mnemonic words but I have no idea if they are still providing this key.
If you have privacy concern, i suggest you to use Desktop wallet, whether it's SPV or full nodes wallet such as Electrum and Bitcoin Core.
Bitcoin core is one of the oldest and trusted wallet of all time but I'm not using it anymore since it requires to download the whole network. Electrum is a good choice but there are also good wallets that are indicated to
https://bitcoin.org/en/choose-your-wallet