Great advice. All hens slow down egg production and eventually quit laying eggs long before their life span is up. So you will need to decide if you are raising them as pets and don't care when they stop laying eggs and you just want to keep them for fun or if you are wanting egg production.
Nope, they can live 10 years or longer depending on the breed. You would need to read up on your breed. I do cull but I don't eat older birds. For me they are just too old and worn out. Others might. I do cull and eat young roosters if no one wants them and of course heritage meat birds I butcher. My hens who lay eggs live out their lives so far but I'm only 3 years in. But I have lost hens to coyotes, hawks, etc. so it's not necessarily old age they die from. Found one hung in the pen one morning. Found one dead in the nest box, found one dead like it had stepped out of the nest box and just fell dead. I always watch my chickens and deal with worms, mites, or "somethings just not right" but still there are sometimes where I just stand there and go "What in the world happened?". If it's something I can correct I get to it right away.
Broodiness does not extend their egg production. As a matter of fact, they don't lay eggs whilst broody and they don't lay eggs longer into their lives if they are broody. Broody is just them wanting to be a momma....some hens (Silkies) seem like they are broody ALL THE TIME, lol.
Chickens that lay an egg almost every day tend to live shorter lives than other chickens.
