I do know that laptops shut off the charging system after the battery reaches 100% charge. How is that any different from turning your laptop off and not plugging it in? If a battery is left on a charger 24/7 (a charger that doesn't shut off after the battery reaches full charge), then yes, the battery will suffer significant capacity loss, but modern chargers (such as those in laptops) monitor the charging process carefully.
Also, having the laptop off when charging? What on earth is the point of that? Charging a battery is usually a low-power process. Unless a battery charger is rapidly charging a battery, it is charging with less power than it will put out. As long as your laptop's power supply isn't too low, it should be perfectly capable of both running the PC and charging the battery at the same time. It would be stupid for a manufacturer not to provide an AC adapter that couldn't do both at the same time, as you plug your laptop in when your battery starts to die so that you can continue working or using your computer.
Again, keeping the battery out of the laptop when not in use...The laptop already does this. Charging current is stopped on most laptops after the battery reaches 100%, so the battery is essentially disconnected. The only thing connected is the monitoring system, which makes sure the battery stays at 100%. Should the power drop lower, the charger may slowly feed it power to bring it back to 100%.