Does removing the laptop batteries and
using the laptop on AC power, having the charger plugged in all
the time, damage your laptop in any way?
I had recently purchased a new laptop. It's my first laptop and I, being a computer geek, definitely know a thing or two about maintaining a PC but this thing had really got me worried.
It's been 4 months and I always use my laptop directly on AC power (removing the battery) unless I am travelling or there is no source around. And of course, I keep in mind the battery usage practices like charging only after battery is reduced to less than 10 % and not keeping the charger plugged in after the charge is completed (in that case, I remove the battery and continue using on AC power). Also I let my battery get discharged completely at least twice a week.
Now the million dollar question - Am I doing it right? I recently read some articles about laptop battery usage and have come across things like - laptop is damaged by removing and inserting battery while it is turned on (when connected to AC power), keep using laptop on battery power and keep discharging & charging battery i.e. never remove battery from laptop and many other such things.
There is nothing wrong with using a laptop with the battery unplugged, but it is completely useless (except of course if you have some specific reason for removing the battery, like it being dead, lending it to a friend, you want to make your laptop lighter, etc.)
I am sorry but the "battery usage practices" you follow are myths. Some of those practices are and always have been simply false information. Some of them were helpful ten years ago with Ni-MH batteries but are totally useless or even harmful on modern lithium-based batteries.
Keeping the battery plugged, or unplugged, or
whatever is useless
Keeping the charged battery in with the AC adapted plugged is perfectly fine. With modern chargers and control electronics, it amounts to the exactly the same thing as storing it charged separately from the computer.
Incomplete charge and discharges are perfectly fine. They are actually better for the HP COMPAQ batteries than full charge/discharge cycles.
Totally charging the battery is useless
Completely discharging the battery should be avoided if possible. Actually, totally discharging the battery cells is extremely harmful to the battery and can cause severe and irreversible capacity loss, but the control electronics in batteries won't let you do that, they will stop the power output before the battery is completely discharged precisely to avoid that problem. (On the other hand, if you discharge a battery then store it empty for an extended period of time, then the problem may manifest and damage your battery.)
If you store an unused battery for a long time, the optimal charge level is around 40%. That will maximize both battery life and the hold of the charge.
It is good to know that lithium batteries are fundamentally unstable and slowly lose capacity as they age, whether you use them or not. They age faster when they are used, but they irremediably start losing capacity the moment they get out of the factory even if they remain unused. A Apple laptop battery built this year will have a higher capacity than a battery built two years ago, even if both are brand new and still in their original packaging. That is good to know when purchasing batteries.