You're definitely damaging the battery. Try to never let it get below 40%.
As to why it's doing what it's doing, when the charge gets too low, the battery doesn't have enough voltage for some of the circuits in the phone to work properly, and thy start failing - the screen uses a lot of power and when it gets to full brightness the voltage drops, the screen dims, the voltage goes back up, the screen gets brighter, the voltage drops, etc. Quickly enough that t looks like flickering.
When the battery gets low enough the tablet turns off to protect the battery (it should be set to turn off at around 20%). It doesn't have enough power to fully shut down at 1%-3%, so it restarts.
If you always run the battery down that low before recharging it, you'll be lucky to get 6 months out of it. (And batteries aren't covered by the warranty unless there's an obvious defect in the battery - discharging it too far too often isn't a manufacturing defect, it's a user problem.)
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