Is it required that in a new home there be a separate circuit for ligthing stairs, hallways and egress routes? How is that defined if so?

Not that I know of.
And what's an egress route in a residential home? All I know of regarding emergency escape for residential homes is based on IRC R310. Now, if you want to install your own emergency escape route, with emergency exit lights (Lights will operate under emergency conditions), then go for it.

Also, check with your local building inspector or AHJ for more information---seeing that your jurisdiction may have a code in place regarding your question.