Hi CraterLakeChick!
1. Yes, it's completely normal. fresh pullets will lay eggs with papery shells, no shells, no yolks, tiny eggs, and even eggs laid inside membranes like little water balloons! It just takes a while for the egg factory to start getting everything in the right order, and it's not unusual for a few steps to get missed along the way when they are first starting out. Make sure you remove all traces of broken eggs and shells from your nest boxes and coop, to ensure no-one gets a taste for egg-eating!
2. I always think it's a good idea to have a separate bowl of oyster shell that the girls can go and pick at as they need to. Make sure they also have access to grit to aid them in their digestion.
3. If you put some golf balls or plastic/ceramic eggs inside the nest boxes, this will help your chickens understand where it is acceptable to lay. Fresh layers usually have 'accidents' outside the nest though. It is very much like toilet training a toddler I have found! The plastic/ceramic eggs also help in discouraging egg-eating and egg-pecking. They have a go at the plastic/ceramic eggs, realise they are getting nowhere, and then leave the real eggs alone when they eventually come.
I also personally think that the half-formed eggs are not 'laid' per se, they sort of slip from the bird when they are not expecting it. I have found a few of these under my roost from time to time, but when the same girls lay a fully formed, shelled egg, it is always in the box.
Finally, I can't quite tell from the picture, but do all of your nest boxes have some sort of bedding in them? It is very important to make sure the girls are nice and comfy in there.
Good luck! May many eggs come your way soon.
Krista.