Regarding the Cory eggs
Cory eggs are laid fertilised, after the female deposits them no further care or action is taken by either the male or female fish. Apparently it is possible to move the eggs, I have never done this. I just move the fish to another tank and take the filter etc, then run an air stone for the eggs. That's fine for 6 weeks or so. (See previous links for pictures etc.) the Flickr page has a full account of breeding corydoras. I was lucky in that I finally managed to document the entire process. Receiving, producing, holding, laying, spawning and growing out.
When I'm purposefully breeding this fish I separate them first to a breeding tank after the eggs are laid the fish are removed.
Additional food, infusoria to begin with, make a culture or buy ready made.
Then as they grow start feeding them larger food stuff. I can explain more if you like? It's all available over the counter but there are some cheaper alternatives.
The eggs and fry are considered food to the parent fish.
Dead eggs will grow fungus.
The batch I bred at Christmas, every egg was white. As far as corydoras paleatus goes, the eggs are normally white until they hatch. I'm not sure I recall seeing brown eggs, but, I haven't bred bronze corydoras.