Battery

I will simplify it for you. To buy a genuine Dell battery, you may buy direct from Dell or from Parts-People. I linked directly to the batteries compatible with your laptop model. Dell has only the 60 Wh battery, while Parts-People has both 60 Wh and 45 Wh batteries, each of which is compatible with your laptop. Don't worry about the voltage difference, both are officially compatible.

While there are some other sources of genuine Dell batteries, many Internet sources supply counterfeit or unofficially "refurbished" batteries of suspect quality.

Whenever touching components or working inside a computer, wear a grounded wrist strap, also called anti-static wrist strap, ESD wrist strap, or ground bracelet. It's a cheap and sensible precaution. Rest the laptop on an anti-static mat or at least a reasonable alternative such as corrugated cardboard.