Why is iPhone battery percentage fluctuating at lower levels?
To recalibrate your iPhones battery, you should:


Use the iPhone until it shuts off due to low battery.
Charge it, without interruptions, to full charge (100%).
Reset the iPhone by Holding Home and the Power buttons at the same time. Ignore the Slide to Power off,  and let the iPhone restart itself.


And for the notifications, as far as I know, no such thing can be achieved without jailbreaking. Cydia's app LowPowerBanner, for instance, should do the trick, though.