You don't have to keep chickens to know this - outside of the U.S. eggs aren't washed before being sold as washing removes the antibacterial cuticle which then means that they need to be refrigerated. Seems like a ridiculous idea to me - wash them to make them more likely to spoil, but of course the best solution is to vaccinate the hens to prevent salmonella contamination.
How long does it take for a chick to hatch from an egg?
About 3 weeks
most chicken eggs (particularly the ones produced for consumption) are not fertilized by a rooster