Hi Mabel - I don't usually check the birding forum (which is for wild bird), so I'm glad I passed by here this morning. Please make additional comments or question in the bird forum, which is in the home and garden category.
The first babies should be pretty much on their own now and can be safely removed from the parent birds. It is quite normal for a 2nd clutch to be laid at this time and if conditions are still good for raising babies when this clutch is almost weaned, you will probably find more eggs in the nest. It is not healthy for the hen to lay a 3rd clutch though and you should think about removing the nestbox as soon as this clutch of youngsters start to leave and before they are ready to go on their own.
If the 1st babies are not eating well on their own yet, you can move their father into the new cage with them for a few days, while the female is left to incubate the eggs.
Are you sure that the 2 dark eggs were not from the first clutch and did not hatch?