lady green singer finch, 1st eggs and balding of breast

Question

girl finch   Hi i have a pair of green singer finches that I have had for 2 years. I have noticed one molt last year that was noticeable by the amount of feathers to clean. I have never had a nest in the cage until recently. they have never mated.
My husband was caring for the birds for a week. I came home and noticed the female had been loosing and picking feathers from her neck and upper breast area. I was concerned so my husband did some research. We found out it could be molting I have never experienced it until I noticed she was pulling out the feathers on her upper breast. A day later there was an egg in the water dish. I put in a nest after that and some nesting material and another egg landed in the nest. they pushed it out and it broke.  Then every other day I found 2 more eggs broken on the floor of the cage. I was worried and put a marble in the nest so that she would stop laying eggs. The male bird is trying to mate. He has never before? She is acting and eating fine, it even looks like some feathers are returning but she is still plucking a bit. Is this brooding? should I take out the nest? I just want her to get better.

Answer
Female birds will pull their feathers to create a soft nest for their babies. So I'm not too worried about that as long as there is a nest and nesting material. As for the eggs on the ground, it sounds like male is kicking them out because he wants to breed her again and because she is laying eggs, she doesn't want to. This shouldn't escalate to anything major (just make sure the female gets plenty of calcium, wind eggs can kill her) but just watch the male closely, he may start getting aggressive