How long can a week old Zebra finch go without food?

I think you should put the female and the nestling in a separate cage with no nesting material. Use cardboard as a nest. Give the female wax worms and see if she feeds the nestling. It is way better than letting the bird go hours without feeding. You can still supplement feeding when you are home, but if the female was trying to feed then give her the job while you are gone. Just do not give her anything that she might try to give the nestling that isn't safe. Do not worry about the night time for 6 hours. Birds sleep too.