Color of eggs (brown, white, blue, etc...) is determined by the breed of chicken.
Hardness of shell is determined by items available for the chickens to ingest (ground oyster shells, etc...-including bits of egg shell, but wouldn't advise giving egg shell- will result in harder shells)
Eggs will remain good for quite awhile without being refrigerated (as already stated). My grandmother didn't bother.
How many eggs a farmer gets in a week will depend on the breed of chicken, what it's fed and the time of year. Winter is the lowest production time. Colder weather = fewer eggs. Warmer weather = more eggs. Unless the chicken is being fed laying mash (or an equivalent) the average for most of the common breeds left free ranging and "living off the land" is around 5 eggs a week during warm weather (so 20 chickens will average around 100 eggs a week during the most productive time of year). From start to finish it takes a chicken 24 hours to create an egg.
It is not uncommon to sell this week any leftover eggs that didn't sell last week. They're still perfectly good eggs and helps keep up with demand when you have a short supply week.
If one of my eggs "floats" it goes to the dogs or to hogs