Haha, i've always called it the window shade. I think the term started in the early days of android
Yeah, Kindle FreeTime can't be deleted. The best you can do is hold down on it until the option pops up to remove it from the carousel. Then, as long as you don't open the app, it
shouldn't come back to the carousel.
Are you sure your wifi was off? The update was pretty large and if you are currently at the latest software update, you must have had wifi on for a while. If its while you were using it, the Kindle would have rebooted on you and you definitely would have noticed!
Either way, as others have said, battery drain over time is normal (wifi or not) and if the battery is all the way dead it won't turn back on until its been plugged into a charger for a few minutes.