https://www.tractorsupply.com/tsc/product/producers-pride-mini-defender-coop-mdc001 This is a cute little pen that would be perfect for my Bantam Feather Foot trio
Hens can be really sneaky and inventive about hiding eggs. They can squeeze into spots and lay eggs that you can't imagine they can get into. Maybe your friend should try keeping them cooped for a day or so to see how many eggs are really getting laid.
You may want to start checking for eggs a couple of times a day. They could be still laying and the rats could be carrying the eggs off before you find them.
Hurricane Irma interrupted egg laying with my girls last year. They quit laying, molted and were back to normal. Storm stress, or maybe just that time of year.
I've usually had adult birds around to teach them to roost. But once they get the idea it like a contest every night to get the best and highest perch.
I like the light idea, I have used it in the past and it has worked. Treats work too if it is something they love; use it only at evening time and they will think of the treats they will get.
Leaving chickens in trees is not really an option where I live because of the tree climbing predators...
I'm sorry to hear about your rooster. I've had that happen, and his hens were freaked for a while, were skittish, quit laying. They do form family groups and the flock is affected by the loss of one of its members.
The game camera is a good idea, in case whatever it is comes back.
Just give...
My older hens do what I call the "eggless song", the the roos join in. The bantams cluck some when they lay, but it's usually the older ones that make most of the noise. They will also start up their clucking and carrying on when they first see me in the morning. Funny birds.
I have some Bantam Cochins I got as Easter Peeps. One is a Black Birchen too I call Spike because he had a little comb at one week of age. Another roo I call Pie because he's big and round and likes to lay flat with his wings spread out, like a round pie with a chicken head sticking up. A third...