Hi barbeau,
It 's not 100% clear from your post, but could it bee your iPad/Phone going into power saving mode when watching the Radar? SkyDemon suppresses this when tracking a flight, but the Radar cannot do this as it uses the default browser. As a workaround, go to Settings>General> Auto-lock, set this to 'Never'.
Yes, it is possible to have a connection to your PAW with WiFi and still have the GSM Mobile Data connection to the internet. I do it, however, there are two issues. GSM Mobile Data does not always work well in flight and you keep getting the GSM chatter in your ears while it tries to connect. So I turn GSM data off in flight. I have never needed to use Bluetooth tethering as Peter suggested. This should just work.