two questions: feather loss and eggs

Question
Hello,

My pair of Zebra finches have laid eggs many times, finally one hatched, but the parents let them die.  Then the next few clutches they would break them open and toss the eggs our of the nest.  Will they ever try to hatch eggs again?

My female has feather loss around her neck.  She has always been a bit of a messy feather look (bed head look) to her. Should I remove her from the cage?  Could she have mites?  They have plenty of nesting material and I do not see feathers being used in the nest. Any help would be appreciated.  Thanks!

Answer
It sounds like they are either too young or just unfit parents. The male will sometimes do this to get the female into breeding again. There really isn't much you can do about this except take the nest away.
It could be mites. The best way to tell is to spread the wing and check the feathers. You will know immediately if they have mites because the state the feathers are in. The website provided will have something to remove the mites