Cornish cross egg laying questions

So This is my first year having my own chickens, I raised some broilers along with my egg layers, and decided to keep one of my smaller cornish cross hens, to breed some of the meatier traits into my dual purpose flock. My birds are free ranging on an acre, and are fed only at dusk, and the feed is gone by dawn. The feed also has a low amount of soy and corn, and my main base is oats, and contains no GMO's. She is currently about 10 lbs at 19 weeks. She isn't as active anymore, but will come running if treats are involved or near dusk! Then she follows everywhere. She also loves to dig around the coop for any bits of feed in the litter.

My question are;
About what age do CX's start to lay? ( I think she is close she has been making nests and we heard egg song from her once last week, but no egg, plus roos are very interseted in her!)
Is there a way to restrict her diet without starving the rest of my birds, or lockink her up? (she has become top hen, mostly due to her size and hogs the food dish)
How much does a heavy breed chicken need to eat in a day?
What are her chances on living to spring?
Do cx's go broody?

welcome to BYC!!!
CX usually lay around 20 weeks or earlier. roos can be hard on them as their legs are already packing so much weight around, you may need to consider how much exposure to them you give her.
I would ook her up while th others eat, then let her out to range and eat the scraps, the more you restrict her diet and encourage free ranging the longer you will have her.
My opinon is that she will find enough on her own to keep herself alive.
the average age reported on here seems to be 12-18 months although Al has some that are over 2 years.