This feature is planned for Gospel Library for Windows 10 (what previously was being called v3, and is now being called v4).
If you're using the current release version of the app (version 2.x), you can already pin bookmarks via the bookmarks pane. The feature will be returning in the beta in the near future.
Initial groundwork for offline media is now in Gospel Library for Windows 10 Beta. You can download media, though the experience is subpar and incomplete at this time. We’ll be working to complete and polish the feature as development continues.
You can learn more about the beta at the link below:
Offline media is only supported for non-embedded content. Embedded videos are still not offline capable. We'll be building on our groundwork in future updates.
We've never said that this feature would be limited to tablets, just that (a year ago), we'd redesigned the interface for tablets to make this more feasible on those devices. That said, this feature will be exclusive to the Windows 10 UWP version of the app when it releases.
While we’d love to be able to support the Chromecast, there isn’t a Windows app SDK for us to use to implement such a feature. We’re waiting on Google for this one.
Gospel Library for Windows 10 already supports DLNA via Windows' casting functionality, so you should be set, there.
We have something similar to this that is planned for the home screen customization feature.