The Dutch breeds Welsummer and Barnevelder and the French Maran can lay a really dark brown egg, but again, they need to be good utility strains. The Speckledy is a modern cross that lays a reasonable number of brown eggs, although they are smaller than those of hybrids. Again, it depends on the breed. Three hybrids will produce enough eggs for the average family. Very well for the first two years, then the number of eggs gradually reduces.
Hens often stop laying while they are moulting and resume when they've grown their new feathers.
They may also stop laying through the winter unless they are given some light to extend the natural daylight hours. The oldest l've heard of was a 15 year old which was a cross-bantam. No, unless your want to breed your own chicks and are far enough away from neighbours likely to complain about noise. Cock crowing is a recognised 'noise nuisance' in law, and you can be forced to get rid of a cockerel if the local authority decides to take action. It's not true that hens lay better when there's a cockerel around.