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?
Your encrypted wallet is automatically backed up to our servers. To safely store your wallet, we add another layer of security by encrypting your wallet a second time. Securely storing your wallet on our servers ensures that you can access your wallet from any (and all) of your different devices.
Your password acts as your decryption key to both lock and unlock your wallet your wallet cannot be accessed without it. Because we dont know or store your password (we cant even reset it), only you are able to unlock and decrypt your wallet.
When you access your wallet with your Wallet ID (a unique identifier specific to your wallet) and password, your browser uses our API to download your encrypted wallet backup, before safely decrypting it on your device.
So I guess Blockchain.info basically does store or keep your private keys/wallet, but in encrypted format. When you access your wallet, the encrypted format from their database is sent over to the browser where it gets decrypted with your password, clientside. There have been many instances of Blockchain wallets getting hacked because of weak passwords/browser plugins. They are a web/hosted wallet, as far as you have a very strong password, I guess they are safe to use, but not the safest.
https://blockchain.info/wallet/how-it-works