It depends on the type of laptop you have.
No, it will not harm the laptop to remove the battery and plug it in if it will run that way.
Of course laptop can run with a battery as long as the battery is in good condition. If you battery have some problem with charge, you may need to buy another one. And you may shop here, i bough one recently, and it runs quite fair.
Battery run-time on a laptop is difficult to determine. Actual battery running time depends upon the power demands made by the equipment. The use of the screen, the hard drive and other accessories results in an additional drain upon the battery, effectively reducing its running time. The total run-time of the laptop battery is also dependent upon the design of the equipment. Generally, a new Hi-Capacity laptop battery will run 30% to 50% longer than the old laptop battery did when it was new.
Run time will vary on individual laptop computers, based on the applications being used (i.e. high graphics, games), the number of times something is saved or retrieved from the hard drive and/or CD Rom drive, the memory of laptop, and chemistry and capacity of the laptop battery. A realistic average run-time for a laptop battery is 1.5 to 3 hours. Again, run time will vary on applications being used and individual laptops.
Your battery may be worn out. When you use electricity to run the laptop your battery should not be in your laptop. The power will run through the battery making it drain. Either replace your battery, or take it to get it check out if it is still under warrenty.
When I plug in my laptop, it does not use the battery to run the computer. Instead, it uses the wall outlet to run the computer and to recharge the battery. So, by leaving my battery in my laptop when it is plugged in, I am recharging my battery and not running it down. If you take the battery out of your laptop and do not recharge it, it will not last long. The computer batteries that I know about can go from 2 to 8 hours without being recharged.
No, you need the battery or there'll be nothing to charge the laptop with! Yes, i can run my laptop without battery and just plug the adapter. And i do so for a month until recently got a new battery. and it's cheap and runs well. Here is where i bought it (related links).
You need to buy a new battery look up which battery works with your laptop and buy it online
Run the battery calibrator
This laptop has a battery life of around 7 hours. This can differ with the type of applications you have going and the power options on your laptop.
run the battery calibrator
its ok to do that but if you do it for too long then the battery wares out