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From someone who has cockerels running with my hens and mating them I can tell you this is not necessary. Even experienced chicken keepers are often unable to tell if an egg is fertile or not, so don't worry that the eggs will look or taste any different. As regards collection and storage, just treat them as normal. Personally I don't refrigerate my eggs. They sit on the counter top until I use them and I have eaten eggs(even fertile eggs) kept at room temperature for over a month and they have been perfectly normal. It is always best to collect eggs daily, but I just recently found a secret nest that 2 of my hens have been laying into for some time and I am in the process of working my way through those (all 43 of them!!!) starting from the ones in the bottom, which I can only assume are the oldest. They are perfectly edible and normal, albeit not as fresh as ones laid today, but still look and taste fine..... and I know that one of the hens laying them is a favourite of my prime cockerel and gets mated very regularly and is fertile because she hatched and raised 14 of her own eggs/chicks last summer, but these eggs have been sitting in a nest for maybe 3 weeks with 2 hens climbing on top and laying another one each day and they have not developed.
Basically, having a rooster makes no real difference until you have a hen that goes broody and even then, it takes a couple of days of a hen's CONSTANT warmth(ie day and night) to effectively "trigger" development.
As regards your other question, I would not leave a hen sitting on eggs that have no hope of hatching or golf balls/fake eggs. Brooding takes a lot out of a hen and if she is committed, she will often set until something hatches....not just 21 days and then give up. It may therefore be kinder to break her of it than let her set for a long time with no chicks at the end of it.
The usual method to break them is to place them in a cage with mesh or slats on the bottom and chock it up a few inches off the ground with no nesting material, so that she has nothing to snuggle into to keep her breast warm and there is air able to circulate underneath her. Make sure she has access to food and water and a roost bar to stand on, especially if you use wire mesh as this can cause sores and frost bite on the feet at this time of year. This should break her of it in a few days.
Best wishes
Barbara