In fact, recent laptops nowadays use Lithium-Ion batteries, which means that the charger will stop after the battery reaches the full charge. So you don't have to worry about the battery and its lifetime if you keep working with the battery in and the power is from AC.
Nevertheless, you can take out the battery and keep running the laptop from AC power, it's up to you.
Now talking about charging non-fully charged batteries, it doesn't matter if the battery is fully discharged or partly discharged; what really matters is the cycles of use... each battery has a limited number of using cycles and differs from one to another. So, every time the battery is fully discharged its lifetime is decreased by a cycle.
From this point I recommend you to use the laptop on AC power as long as you don't have to be away from it.