Could be - but that would also mean taking milk away from the calves for a while. Not sure how much milk a cow would be able to continue to give and what the quality would be after the calf has had enough to outgrow infancy.

This is doable, especially with the cows, that have been bred to produce milk. You do not even need to separate the mom and calf, for more than a moment, to milk, so we do know it is possible. You just get less milk, than by taking the calf away, so it is not profitable in comparison. There are other problems though, like they should be able to feed mostly by pasture grazing, which takes a lot of land, and if you do not kill some of the cows and bulls for food, you will have way too many... etc.

And with eggs - yes. The EU standards for "bio" eggs are already better (very far from perfect though), so it might be possible to do profitably even. A big ethical problem with factory farming chickens right now, though, is the process of mass producing the egg-laying chickens themselves. Hens are kept, but the male chicks might be just thrown into a shredder. Even if all of them were raised, a lot of the cocks would have to be killed, since there would be carnage otherwise, as you cannot keep them together, and you have to have multiple hens more than cocks in a flock. This also applies if you keep chickens in your backyard, so there are always excess cocks being given away, that nobody wants, and many end up as food.