As my primary stationary computer recently broke, and I'm now using my laptop instead, I'm wondering if I should remove my battery from the laptop, when I have my power cord connected, because I don't want to overcharge it and damage it.
My laptop is the Lenovo ThinkPad L430 Laptop.
You won't overcharge it.
You may be able to extend the battery's life by going into the BIOS at boot time and setting the maximum charge to say 80% (if the BIOS supports it)
You are much more likely to do damage (to the disk drive) if you run it without a battery and the power lead is disconnected accidentally.
Most modern laptops will automatically stop power flow to the battery once it's fully charged, but it can't hurt to unplug it from the wall when it's full.
There are few products sold today that do not shut off automatically when full charge is obtained. All laptops auto control charging. Be careful to not strain the jack/jack plug by pulling sideways on it with the adapter.
Some will not function on external power if the battery is removed.
I really don't see what the concern is. Use the laptop on battery, then plug it in when it's getting low.
You can't overcharge a laptop battery.
There are different cycles in the battery charge process as it goes from empty to 100% charge, and, it doesn't actually get fully discharged. The final charge as it goes over 80% charge is a trickle charge. When it reaches full charge the charge cycle stops.
Lenovo has a feature on some Thinkpads to set it to extend the time to replace the battery. The longest lasting battery is held to about 75% charge and there's a likely setting if you normally use it plugged it under power management or battery management. What it means though is to fully charge it to use it for the full time on battery you need to reset that to normal use.
The biggest issue is heat, but with most new laptops with encased batteries they are in worse shape than yours. If you choose to run only on AC power removing the battery there are two cautions and one notation.
1) Plug and unplug wears on the connector. Don't keep removing and putting back the battery. If you go a week at a time without needing the battery it might make sense.
2) Watch use of the laptop. If the power cord unplugs while there's no battery in the laptop, it immediately shuts down, in a method even worse than pushing the power button. Loss of power while in operation can corrupt the registry. When you properly shut down, software is closed properly. In sleep and hibernation, there's a cycle to save settings. But, if the cord falls out, that is an immediate stop, and it does not pick up where you left off. Instead, you cold boot and it normally will boot properly. If using it on AC power without the battery keep the cord from falling out or pulling out.
3) When you remove the battery it is better off not being at 100% charge. And, charge does slowly dissipate so when you use it again it will be at a lower charge than when removed.
In general, it is better just to leave it plugged in, and when the battery life is such that it does not hold sufficient charge, just buy a new battery. They are normally OK for a few years anyway without screwing around in plug and unplug to try to preserve it. It is much worse to cycle full to empty.