Cache (and more) problems with Mendix developer app
The caching issues have been solved in a newer version of the Mendix Developer app, v1.0.7. It's already available in the google play store, should be available soon in the Apple store.
As to the 3-finger tap: I've noticed this when the backend is down, in which case you simply restart the app and you can go back again. Does that work for you?
The Login widget is a known issue, can't give you an ETA on a fix though. For now I suggest you simply login directly to the user you want using the demo user feature instead of going via an anonymous session.
As an addition, the Windows Phone Developer app does not work at all on a Nokia Lumia 735.
Are you using a cachebust on the components.json file also? In the default theme it uses a file like the following: