yes I am using the blockchain.info on my computer but I have been told to try the wallet at
https://greenaddress.it/ which many have said have safer privacy and security mandates.
Blockchain.info in theory should be quite secure. They offer pretty good security features, allowing you and only you to be able to access the private key thus no one else can spend it. However, they have incredibly bad reliability due to their recent downtimes and several security vulnerabilities which could have been avoided. Greenaddress.it is quite a good choice but the android app is slightly buggy for me. I would recommend either Multibit or electrum for the best ease of use as you can easily forget your mnemorics on greenaddress.it.
Yes but you can export a backup of the wallet, and in case they get shut down permanently, or they lose your wallet, you can still recover your funds with another wallet provider.
What if there is a bug in their wallet generation process? That is what I meant by unreliability. This has happened twice and could potential caused thousands of users their entire Bitcoin savings. Greenaddress.it takes a less conventional way that is to use nlocktime but it requires you to wait in the event that they get shut down. Correct me if I'm wrong.