Blockchain.info is 100% safe. They provide options to easily export private keys, so if you fear that website can be shutdown, you can make an offline backup of the wallet.
Not 100%.
If you used the API, Blockchain.info has had access to your private key already. They *could* have stored it server side without your knowledge.
Your browser by default accepts any JS it gets fed. They *could* have made you send your private keys to the server at any instance of when you used Blockchain.info without your knowledge.
Now, I am not saying blockchain.info does that. I have a lot of trust for piuk, but saying it 100% safe is not true.