1) You can check the internet available by the following method as per documentation:
bool QNetworkConfigurationManager::isOnline () const
Returns true if the system is considered to be connected to another device via an active network interface; otherwise returns false.
2) As for the json bits, you could use the json parser in Qt 5 as follows:
JSON Support in Qt
It is simple enough to bundle Qt 5 againt your application, but it will hopefully available on the platform soon.
Qt 5 on BlackBerry 10 - Beyond the Myth
Failing that, it would be very simple to backport those few classes to Qt 4.