Let me explain the 3 cell battery part.
You see, the word battery is a bit overused. The term comes from battery of cells as in group of cells, similar to artillery battery and is commonly used even for one cell batteries. Inside the battery, there are multiple chemical electricity sources which are called cells. Each cell generates electricity and several cells can be used to generate higher voltages or to increase battery capacity, depending on the way they are connected.
In addition to the cells themselves complicated batteries, such as ones used in laptops, usually contain additional circuitry which controls the charge level of each cell in order to avoid cases where in a battery one cell is almost empty and several are fully charged (because such scenario makes charging difficult), to make sure that the battery isn't overheating and to help measure the remaining charge level, report the battery wear level and so on.
So basically the whole point of the circuitry inside the battery is to make the whole battery of cells appear to the rest of the computer as a single cell. This makes construction of the computer easier because there is a barrier between the charger itself and the battery and engineers who work on the computer part of the battery interface make it fit the specification which the battery manufacturer provides and don't have to focus too much on the way battery works. Because of that, it is possible to replace a battery of lower capacity with a battery of higher capacity, or sometimes with a battery made by a different manufacturer.
On a sidenote, I heard that on computers with multiple batteries, windows will show separate icon for each battery, but I have never seen such computer, so I can't tell for sure.