Yeah, 1 month baby can be weaned. In fact my baby birds at that age usually fledge out and take perches. If they don't do that the mom will kick them out. At that age the baby should know how to eat and probably drink, too. My birds can eat on their own around 3 weeks old although they only get smaller seeds and not enough to satisfy them. Their parents obviously feed them the rest.
With respect to training babies,yes, their home right now is their home. If you don't have hawk problem you can start training them at 4 weeks old. First training obviously is food call. Those babies should have learned to associate food call first. Then you try trap training. Then you can allow them to go in and out freely on an exit door. If you were able to home and train those adults you have, then you are experienced. The difference is that the baby birds still can't fly strong enough to disappear. Don't keep those baby birds locked up for 4 months. In fact by 6 or 8 weeks they are already wing strong and that they can get lost if they become too adventurous or get startled and fly off.
Here is what is going on my loft right now. I have 5 weeks old baby right now that just happened to come out today. After lingering on the ground it just try to pick on grass seeds. I think I allowed that baby bird to stay outside for 15 minutes. Then I made a food call. Initially it doesn't know what to do. But it flew up and went to the loft roof, then to the trap door. It doesn't know what to do initially, but I trained that bird trap training last week at 4 weeks old. I continued making that food call and it saw the rest of the birds inside eating so it got encouraged and went inside. Success! This bird will be released again and the time for it to be outside will take longer and longer until my maximum of 2 hours. That baby bird associated food starting around 3 weeks old when they perked when I make food call. I continue food call every time I feed them. During those 4 weeks old I also introduced that bird to see the surroundings by putting that bird on the trap aviary. It was double training at 4 weeks old: trap training and surroundings training. It was food training starting at 3 weeks old. And now flying (attempted) at 5 weeks old. As you get experienced this becomes trivial.
