Well for one you cannot overcharge a laptop battery, they are electronically regulated and when they are full the system stops charging them.
When it comes to laptop batteries don't expect more then 12-18months life, If the battery cells don't break down then the controller circuits embedded in the battery will die.
Luckily you can pick up cheap OEM ones off ebay that are near identical to Genuine ones, last almost the same lifespan and cost a lot less then what a "genuine" (branded one, probably made by the OEM manufactor) will cost you.
If your laptop is brand new and your battery is already dying, get it replaced under warranty. I just means one of the cells has probably collapsed
Laptops won't overcharge the battery, once it's fully charged it just runs off the AC power if plugged in.
I've personally never see a Dell batter last more than 18 months before they hold absolutely no charge, yet I have a 6 year old HP that only lasted about 2hrs on the battery new and still manages about an hour of life. Battery quality seems to vary.