|If you reverse one of the batteries in a string, does that reversed battery recharge?
Yes. While the other batteries in the string will pump positive charge from their negative terminals to their positive terminals, the reversed battery will extract energy from the positive charge as it flows from that battery's positive terminal toward its negative terminal. The charge will lose energy and the battery will gain energy. Some of the battery's additional energy will go into recharging the battery—converting its used chemicals back into their original forms. But some types of batteries are better at recharging than other. Those that aren't meant to be recharged may turn most of this energy into thermal energy and thus waste it.