if you remove the battery, there is a chance that the power plug may come loose during any frequent movements, causing unexpected shutdown and data loss..... the battery in laptop act like a power filter system and an UPS...
When computer is connected to wall outlet it will charge the battery until 100%. Is it harmful to battery if it is kept at 100% charged for long time. This is now becoming an urban myth Once upon a time it might have some basis in fact however with lithium-ion batteries it doesn't matter. For a start, they are not constantly charged, as this would cause an explosion, so they charge to full and then the charging stops.
Some articles state it is best to keep battery at 40-50% when it is not to be used for long time. How to achieve when it is always attached to the computer? That's only required for long term storage when the battery isn't being used to help prevent it aging.
Lithium-ion batteries whether being used or not slowly degrade from the very first day they leave the factory, you might as well have it in the laptop even if you use the mains 99% of the time to get some benefit of an un-interruptible power supply rather than leave it in the box where it will age anyway.