Development of a fertile egg begins when the egg is warmed to incubation temperatures. I do not list a specific temperature, because that can vary a bit. Ideal incubation temperature is 99.5 degrees F but it can vary a bit from that in both directions. Consistently lower temperatures will cause development to take longer; consistently higher temperatures can shorten development time; both of these situations can cause problems in the developing chicks. Slight differences have less affect than larger ones. 99-100 degrees is unlikely to manifest problems, but 97 or 102 is much more likely to affect the developing embryos without completely killing them. For example, low temperatures during early days of incubation can affect the number of toes that develop.
Typically a hen will lay a clutch of say eight to ten eggs, one per day, then she will begin to brood them. They will all hatch at approximately the same time as they all begin developing when she begins incubating, not based upon when she laid them. The first laid egg is no more likely to be the first to hatch than is the one most recently laid.
Viability decreases with the age of the egg, slightly at first, then more pronounced as the egg ages. A week old egg will almost certainly be viable; a five week old egg may be viable, but chances are pretty good that it will not be.