Does any one keep a rooster and 4 hens for egg production to raise you own meat birds from eggs?
My typical laying/breeding flock is one rooster and 6 to 8 hens. I keep them for meat and to play with genetics, the eggs are just a nice side benefit. During the season I typically have over 50 chickens of various sizes, most of them growing to butcher size. You can hatch a lot of chicks from one rooster and four hens.
Do you use CX or some other birds?
I use a mix of dual purpose breeds, often called mutts on here. I have never raised Cornish X or Rangers. My dual purpose mixes do not get nearly as large as Cornish X or Rangers and are typically butchered two to three months later, which means feed costs are higher and the meat has more texture and flavor than the "meat" birds. They are different in many ways.
Do the Cx birds last over years, or should I research some other stock
Many people on here have tried to raise Cornish X or Rangers and breed them. Most are unhappy with the results though Rangers tend to work out better than the Cornish X. If you read that "Toad" thread you'll see they are having challenges. The problem is that the "meat" birds have been bred to pack on a lot of meat quickly and they tend to grow so fast their skeletons break down or their hearts give out, Cornish X moreso than the Rangers. If you can keep them alive they generally get so large the roosters can't breed naturally and you might need to use artificial insemination.
The commercial operations that raise the flocks that lay the eggs that become the Cornish X use restrictive feeding to keep them from growing too large to breed, let alone just fall over dead. It is a very fine balance to feed them enough of the right things so they grow and lay a lot of eggs yet don't get too big. Their techniques in how they manage them are just as important as the genetics that make them grow so fast.
I don't know how long the breeding stock lasts that lays the eggs that become the commercial meat birds but my guess would be not many laying seasons. The commercial egg laying flocks usually are kept for only one or two seasons. The egg productivity drops as they go through molts and it is not worth feeding them through a molt to get that decreased egg production. It is more cost effective to replace them. I'd expect the same for the flocks that produce the eggs that will hatch into meat birds.
Are their eggs any good when not raising them for stock production in late fall and winter?
Their eggs are chicken eggs, nothing wrong with them.
As
@Mosey2003 says the Cornish X or Rangers will not breed true because they are hybrids. But that does not mean that the offspring won't make great meat birds if you can get them. They still have the genetics to put on a lot of meat quickly, much faster than dual purpose breeds. That's why people that try to breed their own have so much trouble, the offspring tends to grow so fast their skeletons break down or their hearts give out. They may not be as efficient as the Cornish X (or Rangers) but they will still beat the pants off of any dual purpose breed for meat if you can keep them alive long enough to breed.
There is absolutely nothing wrong with getting some Cornish X (or Ranger) chicks and raising them for meat. They are extremely efficient at putting on meat. Some people love them, some people hate them. They are different from RIR's so a bit of a learning curve.
RIR's are not known to go broody much. It can happen but it's not likely. If you want to hatch eggs I'd get an incubator.