The issue you are experiencing is probably because your mobile device is linked to the Roku device/TV in your living room and it thinks that you want to watch the content through your device. Have you tried disconnecting the mobile device from your Roku device and seeing if you are still experiencing the issue you are seeing?
So when I disconnect the TV device from the phone (by selecting "forget device"), it just asks me to connect a device and won't let me navigate the app (though I can still see the "what's on", "remote" and "devices" buttons, it doesn't respond to me clicking on them).
When I disconnect the phone from the WiFi to use mobile data instead, it comes up with the rather cool landscape and the robot, saying "oops, no network detected". That's a full-screen thing: all the buttons and options disappear entirely.
Can you please specify what you are seeing? When you are disconnected to your wireless network, what are you seeing when you play content? Can you provide us with a specific content example that you are trying to watch on your mobile device?
I'm completely unable to view content when not connected to WiFi. On the TV (run through the Roku Express), it's unable to play because there's no network. On the app when running on mobile data, it asks me to reconnect to my device: there are no other options or buttons to press apart from "connect to network"
It doesn't appear that the Express has the Fast TV Start feature.
If you are still unable to resolve the issue, please send me a PM (private message) with your Roku account email address, and include the serial number/device ID on the Roku device along with a summary of the issue you are experiencing. I'll be able to pass along your information to our Support team who can assist you further.