From what you've told me, it sounds like you have a hen that's just not a very good layer. She'll lay eggs, but they won't be very consistent... sorry!
your hen has probably gone broody and picked the feathers from her chest so she can make a brood patch to keep her chicks warm. (that's what she thinks anyway)
Yes, the amount of bedding has nothing to do with it. But we were talking about the fact that the hen's egg was cracked in a certain spot every time she laid, I suggested thicker bedding so that it wouldn't drop on the board....
You can clicker train chickens too! I taught mine all sorts of tricks... also, to get them to come near, find a stool and sit outside of the coop. Singing or whistling will draw them near!
er... I don't think you'll like the answer to that one... :P you have to wear disinfected skin-tight gloves and...well...reach in and dislodge it carefully.
1# put vinegar in their water (you can find out how much to put online)
2# a happy hen lays well, is their anything disturbing your hens?
3# give scratch (cracked corn) along with their pellets
4# if you can get one, buy a rooster. they will pick up if a cock is there
5# are they enclosed? if...
does she eat the grit? if she's nearly a year, her cycle can't have started to end!!! It seems like she's using up all the energy to make that one big egg, and laying ones without shells daily.