Running at lower resoloution won't net you any considerable gain in battery life. Even if you run at 1080p at best you may gain 15-20 minutes of SOT. Modern display panels are very power efficient and all the talk about lower res leading to hugely better battery life is misleading. What you'll lose out in clarity and sharpness is worth more than the little SOT you'll gain
You wouldn't gain any battery life whatsoever, it is the backlights that use most of the battery and they would all still be lit, even running at a lower resolution all the pixels in the display are still going to be working to product the image.