So far , it sounds like everything is fine.
Don't put food in the box as that can spoil and make "mommy" or the babies sick.
It sounds like the nest box is working well. "Daddy" is feeding "Mommy" and that is exactly what is supposed to happen.
Having a cuttlebone would be a great source of calcium and The male will feed from it and in turn feed it to the female.
The eggs are usually laid about two days apart. That means that the babies will hatch (if the eggs are fertile) about two days apart after the first one hatches.
About 20 days after the first egg was laid, the eggs will start to hatch. Another one will hatch about every two days until all the viable eggs hatch.
The babies are very tiny and at first should be left alone unless something really major goes wrong.
The parents do a nice job of raising them although occasionally a parent will not feed a baby or will even kill it. Some females are great mothers while some just don't get it.
It only takes 28 days or so after an egg hatches for a parakeet (budgie) to be mature enough to leave the nest. So you can figure on the nest being emptied in four to six weeks after the first egg hatches.
Some things to do: once a week, I like to open the nest box and lightly mist the nest and eggs with clean water. The box needs some extra humidity in it for the eggs to develop peroperly. I am not talking about a soaking, just a light misting.
There may be a need to clean the box out a little even in the middle of the babies growing up. I like to clean out the box a little after about two weeks after the last egg hatches.
You can carefully handle the babies after they are about two weeks old. keep in mind that when one is two weeks old, there are others that are only one week old as they hatched the latest.
It is OK to handle the oldest ones in the nest and put them back.
It is an old wives tale that a bird will not take care of it's babies if a human touches them.
You will probably not have to hand feed a baby keet but if you do, be extremely careful. It is easily possible to kill a baby by handfeeding it incorrectly.
By the way, it is also possible for your female to be sitting on infertile eggs. You can gently hold an egg up to the light and after about a week, you will actually see a dark spot inside the egg and you will see what looks like veins on the inside surface of the egg. If you cn see that, then the eggs are good. If you have any questions about the eggs then just leave them in the nest. they will either hatch or they wont. It is not uncommon for a female to lay a few "duds" and then lay eggs that are good.
If you have any other questions, please feel free to ask.