I use the AC outlet instead of the battery as power source for my laptop. So if i turn off the laptop, should i unplug the power also or just let it stays it the outlet?
It shouldn't hurt your laptop to leave it plugged in. When turned off, most laptops will check their battery's charge. If it is below 100%, the laptop will continue charging. Once it is fully charged (or if it was already at 100%), it will just cut off the power flow. I leave my laptop plugged in nearly 24/7, and it has never caused any harm.