It depends on the individual hen. If you have enough chickens for averages to mean anything, they usually lay pretty well before their first adult molt. After their first adult molt they also lay really well and the eggs are a larger size. After each adult molt after the first, they reduce their laying by maybe 15% or so, though the eggs may get a bit larger. It's generally not that they totally quit laying. They just lay a lot less often.
I have some hens that follow this and some that don't. As I said, it is very individual with each hen. It can also vary a lot depending on heredity. Commercial egg laying hybrids tend to burn out after a good year or so of really good egg laying, though their second year is often as good or better than a lot of the heritage breeds. The commercial ones are more likely to have physical problems though like prolapse or becoming egg bound. They are specifically bred for that one good year.
It can vary a lot with heritage breeds too. Some breeders breed for longevity of laying, but most don't. Hatcheries generally don't breed for longevity either.
As with all things involving living animals, they have tends and tendencies, but all individuals don't read the book on how they are supposed to behave. The 15% a year after the second adult molt is a reasonably good guideline, but it can vary a whole lot with an individual.
Chickens can make a lot of different sounds. People have studied those sounds and tried to understand chicken language (what those sounds mean). Purring is one of those sounds but I don't know what it means.