I've also not experienced anything close to what you've described. You may have some type of hardware issue? In fact, I believe the Nook is one of the best tablets available at its price point. I have the Nook HD+ w/Android 4.0, 8.9" with 1920x1280 HD display, 1.5G dual-core Risc, and have seen these as low as $130. Bought a leather rotatable tablet case and stand for just $12. Also has Bluetooth, so use my Nook with a separate portable wireless keyboard above.
My Nook charges fairly fast with its included charger. And only need to recharge every 5-7 days when using it primarily as a reader, web surfing, and email.
Comes with Chrome browser, and have not had any issues downloading apps from Google Play. Fast downloads and installs. Even have the Kindle App installed, though haven't yet used it. So confused at all the issues you're experiencing?