How does the battery and power adapter interfaced in the laptop?
The battery pack literally charges itself. There is a MCU or battery monitor chip in the battery pack which monitors both the "external voltage" (which is actually the laptop's internal power supply regulated by the power circuitry) and the voltage on the cells. A pair of MOSFETs are used to control electricity both into and out of the cells. They allow both overcurrent (during use) and overvoltage (during charging) protection via the MCU/chip. They also allow connecting the cells to the power supply if the external voltage drops below a certain threshold as measured by a ADC.