B&N has sold a lot of these Nook Touch ereaders recently with the low prices. I have seen no complaints about the battery, either on this forum or on the B&N forum. So perhaps you just have bad luck.
B&N has no e-mail support (just standard replies). You will have to call or chat.
The Nook Touch uses an infrared screen. Anything detected by the infrared beams can trigger the screen. One cause of battery problems mentioned in the past are covers that are just close enough to the screen to prevent the screen from going to energy saving mode.