Yes, chickens should lay one egg a day. Your hens may be too young to lay. How old are they?
You said she has two 'black eyes' and your other birds are showing the same symtoms. Can you upload a picture? This really worries me as it could be anything from bruising caused by pecks from a bully, to an illness effecting the entire flock. Overall, we need more information, as what you've given is very vauge. If you need help on the information needed, the form below is a good place to start. Just fill it out as best you can, and we can work from there :cd
1) What type of bird , age and weight (does the chicken seem or feel lighter or thinner than the others.)
2) What is the behavior, exactly.
3) How long has the bird been exhibiting symptoms?
4) Are other birds exhibiting the same symptoms?
5) Is there any bleeding, injury, broken bones or other sign of trauma.
6) What happened, if anything that you know of, that may have caused the situation.
7) What has the bird been eating and drinking, if at all.
8) How does the poop look? Normal? Bloody? Runny? etc.
9) What has been the treatment you have administered so far?
10 ) What is your intent as far as treatment? For example, do you want to treat completely yourself, or do you need help in stabilizing the bird til you can get to a vet?
11) If you have a picture of the wound or condition, please post it. It may help.
12) Describe the housing/bedding in use