How are series connected batteries of different voltages (or even same voltages) charged "equally"?
How is it that each battery gets charged about "equally"? Shouldn't the first battery the charger "sees" get a stronger charge?


In a series circuit, each element receives the same current, so an equal amount of charge flows into each battery.  The order of the batteries therefore makes no difference.


  How is it that while charging, you might see 6.9V across each 6V battery but see 9.2V across the 8V batteries? In other words, how does it "know" to charge each battery the right amount (voltage and current)?


Each cell has a voltage across it decided by its state of charge.  As the current flows through the cell, the cell is charged, which causes its voltage to increase. Nothing needs to "know" that.  The voltage increases as a consequence of charging.  


  Does the order of the "mixed" voltage batteries matter for charging/discharging? Would it help to occasionally reorder the batteries so the "first" battery in the chain is changed every month or so, or is that order irrelevant?


It is irrelevant because each cell sees only the current applied to it, and that is equal for all cells.