Are laptop cells balanced while charging?
I don't have specific knowledge of any laptop battery charging circuit, but I'd be real surprised if the charger didn't do charge balancing.  If you want good life from lithium cells while getting good performance and not catching fire, you really need to manage each cell separately.

I did work on a commercial battery backup unit once.  There were 8 lithium cells in series.  The voltage across each was measured separately.  Each cell also had a separate shunt resistor that could be turned on independent of the other cells.  During charging, we checked the cell voltages every second, and turned on the shunts around any cell that was above the median voltage.

During discharge there is little you can do.  There is no advantage to draining the high cells to keep pace with the low cells.  You do have to monitor each individual cell voltage, then shut down the whole pack when the lowest one gets to a threshold.

To really do this right, you should measure temperature too.  Adjust the full and empty voltage thresholds as a function of that temperature.