Wow,
I see three "issues" 1. egg eating, 2. laying outside the nesting box and 3. soft shells.
they are inter-related though. Perhaps if the eggs weren't shell-less they wouldn't eat them..but it is a habit that you don't want them to get into IMO. So let's think for the moment they are just disposing of the easy to get excellent food.
Laying in the wrong place...maybe too because of the soft shell....she doesn't get the normal signals... Or does she not want to foul (should I say fowl?) the nesting box. Most likely the former, it must feel very different to be missing the shell. If I understood correctly also the hen you watched laid two eggs in very close succession, both without a shell. (there wouldn't most likely be time and calcium to lay two shelled eggs.....one with and one without would possibly be a more expected occurrance with such close together eggs.
Lastly soft shells. Because I had this problem with a hen I have since culled....I write a variation of this in a lot of posts -- so I'm now lazy, installed it in my charts and quotes page and usually cut-and-paste
Shell-less eggs. I think that there can be a lot of causes for the chicken to loose the ability to create a good shell.
Do they get enough calcium? Free choice oyster shell in a container is good, and crushing the shells of the eggs you use and feeding them back to your flock is good. My chooks prefer egg shells to oyster shells BTW.
Apple Cider vinegar in their water (1TBSP per 1gallon of water) - helps the chicken's digestive system absorb nutrients -- including calcium, it has to do with the pH factor.
Vitamin D3 helps the hen with egg shell production too. I bought a bottle of tablets at WalMart and crushed up one. put it in with some feed and the contents of the shell-less egg (she was making membranes but no shell) - so vitamin D3, and more protein and good quality layer feed with the most calcium of the available feeds, They tended to gobble that down.
Old age, and other factors can interfere with shell production if you think your hens may be approaching the end of their laying period.
Should have added that I pulverized the eggshells in the food processor, so I had a lot of calcium carbonate powder. For my hen, the shell problem was fixed within days...however, she did from time to time need the special treatment to maintain good shells.
Maybe break the problem into three parts and see if getting strong shells again will automatically solve the other two issues....
good luck with it.
Maybe if they are producing too frequent eggs...a little time in darkness could reset the egg clock. And the drop in egg production could be entirely due to egg eating.
Thank you, She is new at this so it makes since she wouldn't get the urge to go to a nesting box. I am going to be keeping a real close eye on her. I wonder if I put a nite light in one of the boxes if the one that is dropping them from the roost will be able to see to go into the box. And stop dropping them on the floor!