Hoovers and McMurray are selling sexed pullets for "Cornish Game Hens." So they really are just females in this case, although "pullet" would be much more accurate than "hen" for a bird that only lives 3 weeks.
I don't know about the ones sold already-butchered in the grocery stores, whether...
The "Cornish Game Hens" in this thread are the usual Cornish Cross broiler chickens, butchered at a younger age than normal.
They have been bred for very fast growth, which tends to cause health problems before they are old enough to lay eggs. So no, they would not be a good choice for layers.
Yes, the lighting should be fine.
For the first few days, any kind of meat bird chicks should also be allowed to free-feed all the time.
https://www.hoovershatchery.com/CornishGameHens.html
"The Cornish Game Hen is a Cornish Cross Broiler pullet that is butchered at 3 weeks of age when they...