What does the hardware do and what does the BSP do? Does the hardware without any additional mcu have the quaternion 6 dof fusion output? Is there any hardware that can combine a compass in the attitude results?

The motion algorithms has two major components to it, sensor fusion and calibration. Sensor fusion runs on the DMP (in hardware), while calibration runs on the micro. The hardware sensors (Gyro, and Accel) detect motion, while the BSP has manages the I2c, Timer, and Non volatile memory interfaces. The hardware does perform 6-axis (dof) sensor fusion through the dedicated DMP computation engine. The next release of Embedded MPL software will enable 9-axis sensor fusion that runs in a fully self contained fashion on the DMP. Currently the DMP does not support 9-axis sensor fusion due to a degraded performance. We are planning to eventually push full 9-axis operation to the DMP.
10 axis (altitude) sensor fusions can be performed on the MCU by taking the 9-axis sensor fusion results from hardware, and combining with altitude information from a pressure sensor.