when discharging, the BMS is monitoring the current flowing out of the battery. if the current exceeds a fixed high level, the logic in those analog parts causes the output FETs to be shut off, this blocks current flowing out of the battery.
also the BMS monitors the cell voltage and if one cell drops below the low voltage cutoff point,the LVC, then the logic tells the output FETs to shut down.
when charging, the BMS controls the charger current going through the BMS to the battery. if the voltage on any cell reaches the high cutoff point, then the charging FET turns off and no more current flows into the battery, preventing it from overcharging.
most BMS like the signalab board, or gary's 4-24 cell BMS thread, use a bypass or shunt resistor to allow current to flow around a cell when it reaches the final, fully charged voltage for that cell, and the current that bypasses the cell creates a voltage drop (V=IR), which is equal to the voltage across the cell it is bypassing in parallel with it. that current is called the shunt current and determines how fast the cells farthest out of balance keep charging since the shunt current is the total charge current then.
the sum of all the voltages equals the charger voltage, so the battery charges up until that voltage peaks when all the bypass or shunt transistors are on, and no more current flows into the cells, or only a tinytiny amount. that's end of charge, and the BMS will shut down the charging current when one of the cells climbs up to the high setpoint, and triggers the charging FET to turn off.
most of the problems people are having appear to be problems with the charger never having a sufficient voltage for the BMS to allow the cells to all charge up fully so that the BMS will shut off before the lowest cells get fully charged, and repeated cycles like this on the new batteries is causing them to go far out of balance so that one cell ends up in LVC in the first few discharges, if not on the first.
hope this helps, maybe someone else can fill it in better for you. or ask more, it's always great to see girls taking an interest in tinkering with stuff. most don't wanna do it because of the cultural oppression but in general i think they are more thoughtful in fixing stuff, and often can do better work. keep it up.