Chickens will lay eggs whether or not they have a cockerel with them.
They will often sit on unfertilised eggs. They have been bred out of natural ovulation and will lay for as long as there are sufficient hours of daylight. Fertilised and unfertilised eggs are good to eat.
The two factors effecting their laying are daylight hours and age. After two years you should eat your chicken (stew it - it will be tough) and get a "point of lay" chicken about 9mths old.