I am completely confused by your questions.
Sjarvis, your understanding of genetics seems flawed--you can't get back to the genes of one bird that easily, and I can't thing of any colour genes in chickens that work like red bird plus white bird = tan bird
"Line" is typically used to mean a particular set of parents and their offspring.
Generations are usually referred to as F1, F2, F3, ... with the numbers indicating the number of generations separating them from the parents. (F1 are children, F2 grandchildren).
Ok let me make this more clear. This is concerning Laying Parent Stock.
1) How can I Identify Parent Stock hens compared with the hens of the parent stock. So Using the example below- Whats the difference between LINE 1 AND LINE 2.
2) Why are the chicks from parent stock useless when it comes to using them to make more chicks.
For example: Line 1 = Parent Stock
Line 2 = Chickens from Parent Stock used for laying business
Line 3 = Chickens from Line 2
Now why are line 3 Chickens not good layers and why cant i reproduce from line 2.
Why wouldn't they be good layers? They should be.
Why can't you reproduce from "line 2"? Or more specifically, why do you think you can't?
Are you asking about why the offspring of sex-links are not sex-linked? (grasping at straws here) Or asking why the breeds that are heavy layers tend to not go broody, producing chicks? (still grasping for straws)
Let's say you take a breed, not a cross. The chicks will all have the same look as their parents--indeed, you may not be able to tell them apart (when mature) if you don't band them.
Birds from exhibition lines of breeds that are known for not going broody sometimes will go broody, but if you want chicks from non-broody birds, you need an incubator.