whats to prevent the kid from turning the phone off and on again to exit the program and get normal access?

I assume this installs itself as a replacement launcher. In which case it'd be the first thing that come up every time the phone boots. I'm pretty sure the "login" step they show is just on initial install.

As others have mentioned, Kyte replaces the default home screen, so whether kids turn off the phone, pull the battery or the app crashes, it'll just restart. The only way to exit is for the parent to put in their password.

Good question. Maybe in the long run they'll be able to bundle this with kid-targeted hardware that's locked down.

I don't know how they would disable that and the home button on a non-rooted phone.

The home button sends an intent that this application would just act as the default receiver for (just like the Amazon Fire tablet does for its custom homescreen), though if they are still giving access to the Market, a kid could install another launcher that responds to that intent and switch out of this app.

Yes, but the intent of Kyte Phone is to make the phone simple.

If the kid can replace the default launcher, she does not need an special UI in the first place.

(If all you want to do is micromanage your kid's life through GPS monitoring, is it possible to install a hidden GPS tracker?)

If the permission system for apps is a whitelist of installed apps the parent has approved, then installing an app from the market wouldn't necessarily allow the newly installed app to run. The new app would just show up on the device-administration page for the parent to see and decide on.

Now, if the kid uses the market to uninstall the Kyte launcher itself... then I'm guessing the stock launcher or a pop-up asking what launcher to use would come up.

Kids don't have access to the Market and parents have to explicitly white-list an application, so there's not much danger there.