Dead eggs are pretty common. Some hens will lay too many and can't incubate them all or for 1 reason or another they just do not develop. I had to throw out a Red Rump egg on the weekend that was dead.
I never 'mess' with birds when they are on eggs or have young. It is called a nest inspection & it must be done to remove any dead eggs or chicks which can cause disease and/or further deaths in the nest not just to the other chicks but also to the parents.
I am so excited! We have 3 bubs so far. I've only had 1 bub before and it died within 2 days of hatching. She's such a calm mum. Stayed in the box watching me while I took about 10 pictures and she let me pet her all without screaming or biting me.