Opening and closing a pair of terminals
Use a normally closed relay. Reasons:


The relay is isolated, just like the optocoupler
The shown circuit will only work when the (voltage) potential of "NC Terminal A" is higher than the (voltage) potential at "NC Terminal B." The relay will work in both ways.
The shown circuit needs to be fed as you already indicate at question 1. The relay solution doesn't need that.
If the circuit between "NC Terminal A" and "NC Terminal B." is unknown (what voltage?, what current?) the relay solution is probably more robust compared to the darlington that may have lower maximum ratings.