You can leg band any bird. Yes they do lay in the nest boxes. I placed wooden eggs in there and it works...
If you free range, are all your birds laying in the coop nests?
I gather eggs at least once a day, usually when I lock up after dark.
When pullets are coming into lay, I gather more often....out of excitement to see who laid what and to gather any thin or soft shells before they make a mess.
Also gather often if I have problem layer, had one hen laying lots of thin and soft shells before going into molt this year.....
....and a pullet who found they were tasty, so was keeping a close eye to keep opportunity low and the nests and other eggs clean.