Yes, you need a good parrot cage because what you have is inadequate and dangerous (the bird would end up with heavy metal poisoning).
Now, you can't wean to just produce, you need to wean to a food that has lower protein and fat than formula but not one that doesn't have any. The bird will end up dead if that's all it eats. You need to offer two types of soft food served fresh daily. I always recommend one of them to be gloop because this is what I feed all my adult birds and it works out great both for them and babies, and the other one can be polenta or steel-cut oats cooked and mixed with pureed veggies and fruits (baby food is great for this), some nice, good quality, multi-grain bread, birdy bread, etc. Two soft foods, a different fruit, veggie and leafy green every day and some nice soft seeds for dinner will do the trick.
As to her wanting to be with you all the time... well, she is very young baby and all babies need to be with their parents. Notice that I say 'need' and not 'want' because want is optional but need is not. Baby birds stay with their parents for many, many months after they are born and that means 24/7! Because pet birds are stolen from their parents when they are very young babies in the nest and handfed by humans to make them imprint to us, they see us as their family and so they want to be with us all the time. You, my dear, are now a mother and your baby needs you all the time so welcome to the wonderful world of parrot keeping
