Battery and alt questions

1) no - alts produce current as needed, not just because they can.

2) Under normal circumstances the Alt is the only component supplying power in the system - it does all the charging.  Fully charged batt is <13v while alt voltage is generally mid 14's.  Voltage difference between the two batteries should be minimal, always less than the alt, and they will equalize -- neither will charge the other.  There are two instances where the alt isn't the source -- 1) moments of current demand when the alt is too slow to respond and 2) moments when the alts output is exceeded.  At all other times the batts are just absorbing charge from the alt.

3) no

4) no