hi, first off you dont need an air pump with co2 it will just dissolve the co2 straight away, if you are using a pressurized system then yes you should have a solenoid fitted on a timer with your lights.
Some people use the airstone at night to create more surface aggitation as the plants use oxygen at night.
I use the nutrafin CO2 and dont use an airstone at night. However keep an eye on your fish and if you notice them breathing fast or gasping for air then use the airstone
I run both my CO2 systems 24/7 without airstones, and the fish are fine. Some people like to run one or shut off the CO2 at night but in my experience, its not necessary. Only issue is that on larger tanks the CO2 cylinder runs out quickly!