1) Settings (if it's not on the tablet's main page, it will be in the app drawer which is usually represented by an icon of four boxes by four boxes,positioned in the center at the bottom of the screen). The Settings icon usually looks like a gear. From there, scroll through the options on the left until you see Application Manager. Pick that, then on the right scroll through the applications until you find Gospel Library, and tap on that. In there will be buttons for "Clear Data" (will wipe out the entire library content and require re-downloading) and "Clear Cache" - I'm not 100% certain what this clears, but it's not the library or annotations - maybe just your settings, so you'd have to re-enter your login name and set up your preferences again. (Clearing data clears the cache too.)
2) Well, that's pretty much your answer. It must be device-specific, cuz I teach youth Sunday School and have used November videos and can get at December videos.
Yes, I was about to suggest downloading them on a computer, or someone else's tablet.

Hopefully they'll get the problem fixed soon. If you haven't sent a bug report via your install of GL (Help > Feedback), it might actually help them fix it cuz it sends them technical details about your device and OS version...
FWIW,
Liz