We are new to chickens, and were given a flock of 5 two year old hens a few weeks ago, with no background info on them other than age. I am really worried about one of the birds, an Ameraucana) as when she arrived, she looked as though she had diarrhea in the feathers below her vent. Since then, I believe she has laid a few eggs, but she didn't lay them in the nest, but while (roosting?) sitting on a bar in the top of the coop and they broke on the floor. The last 3 were laid in the same way, but they were soft shelled, and just splattered on the floor. I have reason to believe they are her eggs, as they are blue and she is our only Ameraucana (the rest of the flock are; 2 Rhode Island Reds, 1 Buff Orpington, and 1 Plymouth Rock). Today, the other chickens appeared to be pecking something from her face and neck. I picked her up to see if it was mites, and could find nothing, but she just looks kind of sickly, and was just letting the other chickens pull at her head/neck feathers, like they were preening her, but it seemed kind of rough. So I am concerned that the "diarrhea" may be Vent Gleet, after some internet searching. Also, I'm really concerned about the soft shelled eggs. For what it's worth, we are feeding them organic layer feed, occasional ground oyster shells and chicken egg shells (washed, of course), and fowl treat mix (sunflower seeds, corn, etc.). They have a coop to roost in at night but are mostly free range around our yard, where they like to eat bugs and fallen plums. They don't have access to any chemicals or poisons. Here are some pictures, thanks in advance for any advice you can give.