So focusing on the 'Generator remote start/stop' function of the 'Dry Contact' connector, they speak of the relay being NO/NC (normally open vs normally closed) terminals, so that means it has 3 secondary-side switching relay terminals on it (Pin 5 is Common, Pin 5 to 6 may be NO, and pin 5 to 7 may be NC)... Normally, typically means when relay primary coil is off (relaxed).
One terminal goes to the pivot (Common) of the switch. Another terminal for the NC means it is closed to the pivot terminal (Common) when the relay is not engaged, and the 3rd terminal NO, will become closed to the pivot (Common) terminal when relay is engaged (when this engages, it opens the NC terminal. The pivot (Common) just pivots back and forth between the NC and NO terminals when the relay primary coil is engaged or relaxed.
EDIT:
So it sounds like when the battery gets low, Pins 5 to 6 are opened (5 and 7 are closed), and when battery is full Pins 5 to 6 are closed (5 to 7 are open).
The last part (which has poor translation) where they show: 125Vac/1A, 230Vac/1A, 30Vdc/1A, is just letting you know the current limits you are allowed to run across Pins 5,6,7 (at the 3 listed voltage ratings), so you don't burn up the contacts. It basically means don't run a load more than 1A across those terminals.
