Recently I added my paper wallet address and private key to my blockchain.info account. Now I cannot find an option in the app or in the website to delete the imported private key, does that mean that blockchain.info now holds my private key? In that case, I won't be able to add my wallet into another similar app because it's already synced with blockchain.info with my private keys! I am new to this whole bitcoin thing so I am still trying to figure things out. Regards, Bince
does that mean that blockchain.info now holds my private key?
Yes, but not exclusively. You still have your private key on paper, so you still hold it. If you don't (i.e. you lost your paper wallet or destroyed it), you can still get your private key from blockchain.info.
In that case, I won't be able to add my wallet into another similar app because it's already synced with blockchain.info with my private keys!
No, that is not how Bitcoin works. Anyone who holds the private key can spend your Bitcoin. You also hold it on your paper wallet, so you can still import it into another wallet software. There is nothing that prevents you from doing that; it's not like something that can only be imported once.
If you don't want blockchain.info to have your private key, just make a new paper wallet and send your Bitcoin there from blockchain.info. If you want to access your Bitcoin from a different wallet than blockchain.info, then just import your private key into a different wallet.
The private key is a 256-bit integer used to generate a public key. A bitcoin wallet address is a hashed version of your public key. The private key allows you to sign transactions (send BTC to another address).
With the private key of a given address you can sign any transaction, anywhere.
That means that if you have that private key, you can use it in any wallet. Although blockchain.info stores your private key now, you still have it, so you can import it on any other wallet.
The safest possible thing you could do is to send the money from your blockchain.info wallet to your local wallet in a normal Bitcoin transaction. This might be a few bucks, but it is worth the peace of mind.
You could delete your blockchain.info account and then open another one if you like, but this is no guarantee that they will delete your private key. I advise sending an email to Blockchain.info asking what their policy is on keeping and removing private keys.
In general, it is best not to import private keys from wallets that you do not have full control over. You don't know what they are going to do with your private keys and the sure fire way to safeguard your money is to just send it to a wallet you have FULL CONTROL OVER using a normal Bitcoin transaction.