The female will spend up to ten days in the nesting box before producing eggs. During this time she will emerge to poo and to nibble on her mineral block. This would be the ideal time for you to check on progress in the box and to remove egg shells or dead chicks (always with clean hands). Otherwise, she will stay put.
The hen lays four to ten eggs, with one every two days, and each one needs incubating for 18 days (occasionally a little longer), after which they hatch. Sometimes she will only settle in for full-time incubating when the second egg has been laid. Any egg unhatched after 23 days is not going to produce a chick. An emerging chick can take several hours to break free of his shell, and this is perfectly natural, so don’t be tempted to intervene.
Any egg laid after the sixth one is in danger of having its chick trampled by older, larger siblings, which could damage the younger one's fragile body or, at the very least, prevent it from receiving food. In these circumstances you should give the younger birds to a foster mother, if possible, or hand-feed them.
A hen will occasionally lay an infertile egg. This is a sign that her hormones have gone through the mating season motions in the absence of a male, and is nothing to worry about. The hen will not fret or attempt to incubate the egg. Simply remove it, and that’s that.