2. If the wallet is provided by blockchain, what exporting could protect? they already have the key, they are only a target to hackers to get the key
Exporting is for backup. If blockchain.info gets hacked and goes offline you may need your backup to recover your bitcoins. The hackers will only get your bitcoins if you've used a weak password or if you give you password to them.
It is not jailbroken, the app have open source code that i inspected and installed myself (I'm a developer), there is not an easy way to unlock the phone (finger or device passcode, app passcode) and it is always with me.
Is it still not trustworthy?
Depends on what you mean by trustworthy. I assume you're quite comfortable holding a few bitcoins on your phone. How do you feel about converting your life savings into bitcoins and putting it all on the phone?
Cold storage is an essential tool for Bitcoin businesses such as exchanges and highly recommended to investors who wish to take a sizable position in Bitcoin. If you're just experimenting with Bitcoin then you should have no problem.