Most laptops now have a means of monitoring the battery's state of charge, obviously the blinking LED is part of this system. Without having read through the user manual I can't guarantee that the LED will stop flashing, but I would be willing to bet it does. As far as the laptop notifying you about replacing the battery, once again I would need to read the user manual before I could answer that.
You should need to unplug the power adapter at night. It is plugged into a surge protector which will provide a modicum of voltage spike protection.
The battery you have will go through between 300 - 500 charge cycles. The battery is a six cell Io-Ion battery with a voltage of 11.1V DC with a 5200 mAh.
I would still suggest that you have a friend take a look at the output voltage of the power adapter just to be sure this isn't contributing to the battery failure.
Just for the record, I had to replace my wife's Toshiba laptop battery after five years of daily use.