What is the purpose of this NPN transistor in a battery protection circuit?
I tried to redraw  the schematic so it matches the HY2120 application diagram.  







simulate this circuit &ndash; Schematic created using CircuitLab

Instead of using the RDS(on) of (Q3||Q4)+(Q8||Q9), the author decided to use R14||R15 as current sense resistors.


  I don't understand why the author has not just directly connected the VSS pin to ground.  


There is no ground reference in the author's schematic. But there is indeed a reason the author separated the B- and the P- connections.  

B+ and P+ are connected. If B- and P- were connected as well and a reverse voltage was applied to P+ and P-, then this reverse voltage is also directly seen by the batteries.
The author added 2 reverse polarity protections:


D1, a 1SMA5924BT3G, a 9.1V Zener diode of 1.5W which will be forward biased and will (temporarily) clamp the voltage to some forward voltage (about 1.5-2V??) and will hopefully trigger a circuit breaker before the zener blows (because the forward voltage is already 1.2 V at 200 mA, it is likely it will blow quite easily).
The red encircled subcircuit. I think the author makes use of the internal clamping diode of the HY2120. (I assume there is a clamping diode based on the Absolute Maximum Ratings: Input voltage between VDD and VSS pin: VSS-0.3 to VSS+10 V)
Because P- is positive wrt BP+, D2 and the clamping diode are forward biased and Q7 will turn on. Q7 makes sure mosfets Q8 and Q9 are turned off. They have to be turned off, because the body diodes of Q3 and Q4 are forward biased.


Although it probably works, I think using an unspecified clamping diode for this protection circuit is bad practice.