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Actually, getting the code from the server (and caching it) and storing data locally is already a solved problem. Take a look at IndexedDB, which is already supported by Firefox 4.

The idea here is to think of apps as being built on web technologies but don't think of them as being delivered like and acting entirely like today's most common webapps.

Beyond B2G, Mozilla is exploring what it means to be a "web technology-based app" and interesting things are already coming of the project and even more interesting things are yet to come.

https://apps.mozillalabs.com/

>>Apps can be delivered over the web, but data is stored locally. If it is backed up remotely, then it is encrypted first. If our app communicates with other users, then it does so P2P instead of through a central service.

I really wish this to happen. But unfortunately your next statement,

These steps would ensure the company whose app we use only knows that we are using the app, and not what our data is or who else we are interacting with.

clearly says why it wont happen.

What you're describing is very similar to W3C's Widgets: http://www.w3.org/TR/widgets/

Widgets are zipped up HTML/CSS/JS files so can easily be emailed / bluetoothed between phones. Communicating with other users is a bit harder but HTML5 Device APIs should provide what we need in time.