Overdue question is a question that is already waiting for X% of its interval (I'm not sure about the value of X now, probably around 20). So when you add new cards, they become overdue quite quickly, but that's the point of quick repetitions - you just should answer before you forget. Once your interval becomes a couple of days or more (which happens after just 5 or so correct answers if you answer correctly each time) you probably won't hear the sound anymore - you will usually just answer cards before they have a chance to become overdue. As for "long overdue", there is no such thing in the app, maybe just the string could be improved if this is confusing.
The cloud backup is provided by Android and works automagically, I don't even know the details, I just use the API. And I verified that after installing the app on another phone, the data just gets there. However the app definitely shouldn't be used on two of your devices at the same time, I think the backup would get all messed up. So this is useful in case of accidental uninstallation of the app, or moving to a new phone.
There is also option of a local backup and restore to SD card, but it's not polished enough yet to make it available in the UI, so this will most probably come in the future.
Hmm, I'll investigate the Play Store, but definitely not yet. First I don't have time for this, and second, things like local backup and at least some form of import, should be there from the very beginning I guess, otherwise folk will just flood comments with "poor app, no importing, one star, uninstalling"
EDIT: As for the algorithm of changing the repetition interval, one bad answer cancels more or less three good answers. My experiments showed that this is generally a good value, but could probably be configurable. BTW, did you notice the "almost knew it" option, accessible as the icon on the bottom of the screen when answering a card? As the mini-tutorial says, long-press icons to learn what they mean.