Broken eggs ARE pretty smelly, even if they were on the side of fresh or after just a couple days incubation.
If you really want those eggs to hatch, go ahead candle and wash the fertile ones. Be careful not to turn the eggs around too much and use pretty warm but not hot water. The eggs that either did not get covered or just got a few splatters probably don't need to be washed. I suspect there may be protests to this.. but I have done this and they went on to hatch. Candling will answer your concern about the eggs.. if they turn out to be infertile or died, you can simply go ahead and replace all of the eggs. Just be sure all the eggs intended to hatch were set at the same time.
Common reasons for broken eggs in a nest are too many eggs or intrusions- usually by another hen attempting to lay in the same nest. If there are eggs continually added to the nest, that may be the problem. If it is not going to be easy to close off access to the nest, then it will be best to pretty much grin and bear it and be sure to collect any new eggs daily.
For her, probably a maximum of 10 eggs is best.. less may be better such as 8. If there were 15 or more and you are seeing either visible eggs when she is sitting or the nest is literally a pile of eggs, with some on top of others, it is pretty likely that is the problem. If a hen sees an egg that is not under her, often times they will strain and strain to tuck the egg under her and also try to press all the eggs under her.. which can break an egg or two.
I strongly disagree with placing food and water close to any setting hen. On the free range, that is basically attracting unwanted attention to the nest, either by other birds or even predators or pests. Even in a coop, if mice or rats are present it will attract them to her spot.. and either bother her during the night or again attract the other birds to hang around and make a mess out of her area.. especially if she is not the dominant bird. Some birds will poop on the nest if she has food and water within reach of their nest.. not a good thing.
Hens should be getting OFF the nest at least once a day anyways, so she can excerise, preen a bit and go to the bathroom- away from the nest. Even if a hen actually refuses to leave the nest, that is not good reason to put food and water by her.. lift her off the nest and carry her off to the food spot or at least she poops and eats something before being allowed to go back to the nest. Not doing that is just asking for the hen to atrophy. Atrophy is lack of muscle excerise and if she is not maintaining her muscles, she is not as able to keep her eggs warm.