Batteries should be stored at 40% charge. Its no harm to keep it out of the computer.

What is probably hardest on the battery is when you are unplugged for a short time (whether using the laptop or not) because the battery will immediately begin to discharge. Then plugging in later, causes the battery to charge again. This creates more wear on the battery. If your not using the battery removing it is probably the best thing to do, especially if your not going to need the battery for an extended period. It is not a good idea to go for more than a couple of weeks without recharging your battery. If the battery becomes overly discharged ,it could damage the battery. The battery discharges by itself. "Stand loss" is a term used to describe the "amount of charge" a fully charged battery will lose per day when the battery is left in an unplugged but powered off computer or when the battery is charged and then removed from the computer and allowed to discharge on it's own. If you run your computer without the battery you will not have the benefit of battery backup in case of a power failure.

Heat from a machine like a 9100 is probably not good for the battery over a long period of time. Exercise the battery one a week or so. But again u do loose the UPS function.