Is it possible to develop an app that could sniff all the outgoing http packets of a WI-FI network without the need of the device to be rooted? I know there are similar apps like shark for root but they all require the devices to be rooted...
Best regards
Android PCAP developers say "not yet", maybe not ever.
http://www.kismetwireless.net/android-pcap/
Capturing from the internal Wi-Fi on Android is not typically possible.
There are projects which are trying to hack in support for this, and when it becomes more stable, Android PCAP will attempt to support it, but currently these hacks require custom ROMs, specific phones, and root access.
But more generally, in order to put a network device into promiscuous mode, you have to have a driver that implements the function. In Android, even if the driver implements it, the operating system has to be configured to access it, which it doesn't in stock distributions. So without an operating system compiled to access the driver, and maybe including a custom driver, and a phone/tab with the right radio chip, it isn't going to happen.