1) my battery let up after 3.5 years on my Macbook Pro. What you describe seems very similar. When they diagnosed it at the store they asked if if I left it plugged in all the time. My answer was yes... it mostly stays at work and I do leave it on all the time. They told me that the laptops are designed to discharge and recharge on a regular basis. In the whole time of ownership it only reached -40% 3 times. Not a good thing. Cost me about $125.00 to buy a new battery and have them install it though you could do the same ordering from New Egg and install yourself. Save $25.00.
I let it run down a bit nowadays.
2) your charger is bad. When and if you get the laptop checked bring your charger too.