They could have babies pretty much anytime. If you don't want babies you can just throw the eggs out as soon as the hen lays; before the chick forms in the egg. If you do want babies make sure you provide a nest.
YES! and that too!You definitely DO NOT want to just throw the eggs away unless you replace them wood wooden or plastic ones. It's very important to the health of the hen, that she complete the incubation process and give her body that rest.
It's critical that you give them oyster shell and grit, each in a small separate dish and always available. The oyster shell provides the calcium the hen needs to lay strong shelled eggs.
Most Pigeons enjoy leafy greens such as spinach, romaine, and kale.
You will avoid many problems if you keep their enclosure very clean and give fresh water and food daily. You will also avoid many problems if you DON"T let them breed because soon you will be overwhelmed. Pigeons can live up to 20 years and so this is a long term commitment and not one to be taken lightly.