As a user, is there a way to know if the page displayed in a webview inside an application is using https or not?
If you control the network, you can use Shark for Root to check whether the apps open port 80 (default port for HTTP) or port 443 (default port for HTTPS). IIRC, WireShark can also read HTTP headers.
If you don't want to root your phone, and you're on a Wifi network that you owned; you can use Wireshark/Firesheep to snoop on the traffic of the Android device from your laptop.
I don't think there is a way to find out directly. The only thing I can think of is
- Check the log files and hope there is a mention of https, however this is not likely to be very succesful.
- Reverse engineer the app and look at the source code but to understand what your looking for you'll want to have some Android programming experience.