A lot of people that free range there turkeys will not be finding eggs, even though they are laying everyday. If your turkeys are locked up, and you do not have any eggs yet, you should be seeing some in the next month if your feeding correctly. Make sure they are on a good Turkey Breeder feed. They should never be out of food or water. I up there protein (turkey starter) if they need a boost and feed them all the extra eggs (boiled) and grated carrots.
Your first eggs are going to be small. Early in the year, many toms are not fertile even if they do the deed. Fertility increases as the year goes on, and then declines again in the fall if your hens are still laying. I don't hatch the small eggs. But that is up you. The small eggs hatch out poults that will never reach there genetic potential that their siblings will reach. You can still eat them or sell them to someone that wants a pet. They will cost you more because their feed conversion will be poor. They are also not a hardy as turkeys from eggs from older turkeys. Your best breeders are going to be from second year or older birds.
I use my wine cooler set at 55 to store my eggs. I turn them daily and have a pan of water to increase the humidity. Hatching eggs should be collected soon after lay and maintained at 50-65o F. The eggs must not warm to above 65o F. unless they are being prepared for immediate incubation. Relative humidity in the storage facility should be maintained at 70-80 percent and daily egg turning or repositioning is recommended to prevent the yolk from sticking to the inside surface of the shell. Normal refrigeration is to cold and pulls moisture from the eggs. Some people bag the eggs to help keep them from drying out. Humidity should be kept as high as possible during storage, but not so high as to promote moisture settling on the eggs or eggs "sweating" once they are removed from the cooler for transport. Both of these issues encourage bacterial growth. Most coolers can be maintained at a humidity of 75% without the above concerns taking place. Storing eggs for more than 1 week is known to increase embryonic abnormalities and mortality. Some turkey eggs will survive for 4 weeks. Eggs stored longer than 1 week also show reduced hatchability and an increase in the amount of incubation time required to hatch. For each day stored, add one hour to the hatching time. Post-hatch growth and quality of chicks and poults from eggs stored for long periods also suffers. The poults will also need to eat sooner than eggs that are not stored longer than a week. Most will need to eat within 24 hours instead of the normal 72 hours. In both chickens and turkeys, research on incubation ( pre-warming) of freshly laid eggs prior to any storage has helped to reduce the negative effects of extended storage.