Not About Cockatiels but In Need Of Opinions

So I impulsively bought a male zebra finch because I didnt have the heart to leave him all alone in a plastic pet store box. I realized I needed to get him some company so I later bought two society finches (whom I thought were males as well) to keep him company. I put in a wicker hanging nest and before I knew it several eggs had been laid - pleasant surprise? I wasnt really familiar with these birds or prepared for the situation so I hadnt expected breeding to occur, at least not that quickly. Ive scavenged the web for any info I can get on how to handle the situation, however, ive come up empty handed with a couple of things that worry me. I have periodically checked the nest and I see that a few of the eggs have not hatched but I do have some babies that are growing in size. Ive included a high calcium diet with crushed cuttlebone and grit for the mother to feed. My current issue is what I need to do about getting the infertile eggs out of the nest. I also need to know how I can clean it out as it is getting very messy with droppings and I dont want the babies to get sick. The problem with this is that I dont want to disturb the nest in a way that makes the parents reject the babies but I also would like to make space for them and establish a clean environment whilst they are maturing. The nest is a wicker sphere with a small hole in the front so its nearly impossible to do much of anything without disruption. What can I do, if anything? Any pointers would be greatly appreciated! Thanks, Isabella