When the brooder starts laying again is it normal sized eggs or do they go back to pullet size?
Normal size.
And if they don't get broody and another hen lays on the eggs do the original hen go back to laying faster?
Not totally sure what you mean here but I think the right answer is no. Whether a different hen goes broody or not should not have any effect on another hen laying eggs. After they stop being broody they have to get their body in shape to lay eggs. They add on excess fat before they start to lay, that excess fat is mostly what they live on when they go broody so they can stay on the nest instead of needing to look for food. They have to make some changes to their internal plumbing, it's different when they are laying or not laying. They need to grow ova to a size to become the yolk of a new egg. All this takes time.
