Okay- I will answer your original post and additional questions.
Females don't usually hatch eggs in winter, but if the weather is warm and that is when they were born, they might sit. You can also candle the eggs and incubate the fertile ones yourself. In spring and summer, Cayugas are often very dependable mothers and hatch their own. They take time to build up a nest though, and then start sitting after they are satisfied there are enough eggs. *If your hen can't cover all the eggs with her body, when she leaves for a drink or snack or bath, remove the dirtiest and infertile ones so she can cover them all completely.
And you should let her sit the full term (26-32 days from the time ALL the eggs were finally laid) After 32 days, remove the eggs as they are infertile. Throughout her term, whenever she leaves the nest (she should do so daily for food, water, and a bath), remove any rotten or smelly eggs. (Try not to disturb them too much, only do this the first and third week, and maybe the fourth).
As for selling the drakes, it's up to you. If they are both friendly and good, and healthy, you should pick the most colorful if you want good sale on your extra ducklings. If yu are more interested in dual purpose or meat, pick the bigger one. And if one is unhealthy, aggressive, high strung, get rid of it for sure.
And duck eggs can be kept for eating up to 2 or 3 months (if refridgerated) and still be good. Fertile eggs (if not smelly) are good for 10-20 days, rarely 30 (I'd assume) when left outside. HOWEVER, if you "store" the eggs at the right humidity and temperature for a week before incubating them (typically artificially in this case) it improves the hatch rate, and they can be kept up to 4 weeks after.