I have read before that some budgies just aren't good with breeding. If you can work out which bird it is it might be best not to breed with them anymore. You might be able to give that bird a brake and try again in a couple of months once it has matured some more.
It is recommended to let budgies have 1-2 clutches.
If you are wanting to stop this, just remove the eggs from the nest once you notice them. Once the babies have left the nest, block the hole or remove the box so the female can no longer get in.
Are they still attacking him? If they are I would suggest removing him to avoid any injuries. Budgies can be quiet aggressive when they want to be, keep an eye on them and if they aren't fighting leave them but if they become aggressive again I would remove the male
What colours have you got?
My favourite part of the babies are when they are around this age and you get that nice surprise of the colour coming through the tail and the stomach
Are you able to get a picture just focussing on the cere?
From the pictures provided the cere looks pink which makes me think male but it also appears to have some white on it which could be a female.
We can't help you with the gender without a picture as it's just guessing by description. It is much easier to pick up things with the cere with a picture.
Budgies will breed all year around if allowed but it is not advised to breed them when temperatures are high.
Separating the birds can be done for a week or longer, just makes the birds eager to greet the opposite sex when introduced back together
Often the budgies will be hesitant to try new foods but if they have a bird eating it they will try it and notice that it actually taste good. Hopefully the baby is going good