I am a long term budgie breeder, except that I stopped the last 2 years and have just been enjoying my chirpin beauties! Anyway, they usually won't just set on eggs in the bottom of the cage like that, but it's cool they are taking care of them. They usually start setting after the first 2 or 3 are layed, and so the first ones hatch near the same time. After that, they hatch every other day if all are fertile, because they are layed every other day. The eggs can hatch from 17-21 days after they were layed, but if mom wasn't setting until 3 were laid, then it could be up to 26 days from when the first egg was laid til it hatches.
One problem I had when I bred in the small pet keet cages, was that sometimes the mom will kill her babies as they leave the nest and start flying. I think this has to do with overcrowding, because I never have had this problem once I went to laregr cages and then to a large walk-in aviary. At the end when I had these small cages, I just would take out the mother when the babies were 4 weeks old, and let the father finish taking care of them. It is always the hens in the budgie world that end up being murderous, and I would hate for you to experience that!
Whole wheat bread is great to give budgies, and of course all the veggies that are good for us. No chocolate or avocado! They are poisonous.
They really need some sunlight at least part of the day, but I don't think I would move them while dealing with eggs/babies. You probably shouldn't touch the babies at all that small--they are so delicate when they hatch, with a tiny head the size of a pea, and can take a chill super easy. Ideal would be if you were to get a full spectrum fluorescent bulb and put it right on top of that cage to get them some vitamin D before they move outside.