1. Generally, yes.
2. If they are hens, yes.
3. Mostly, yes.
Eggs are the product of the hen's ovulation cycle, and will occur whether there is a c�ck present or not. Fertilisation of the egg occurs internally before the shell develops.
All but an extremely tiny percentage of commercial egg production will be unfertilised eggs. Occasionally, a male chick will be incorrectly sexed and, instead of ending up as 'hatchery waste' (ie. being gassed and ground up into fertiliser / animal feed within hours of hatching) - it will end up with hens in a barn / deep litter / or battery unit. In these cases, there is a chance that eggs can become fertilised.