I'm pretty sure, that both cow and calf are screaming when they are separated shortly after birth. Alnost like a mother and her baby have an emotional bond.
And even the smallest farm will absolutely kill them once they aren't profitable anymore, or they'd have an ever increasing population of animals.
Ummm.... We don't typically have just one pen or pasture for the animals. The males and females are typically kept separate from each other, except for when we specifically want more animals.
We didn't have cattle. Just horses, sheep, goats, chickens, ducks, a couple turkeys, and rabbits.... Tons of rabbits accidentally one time. We let them do their thing when we wanted more.