Hi,
First, you need to split these birds up for now because they are both too young to be breeding already. A male cockatiel needs to be a minimum of 18 months old and the female needs to be at least 2 years old. Birds will mature much more quickly in captivity than in the wild, but if you let them breed when they are too young, you see problems like what you are having. Both birds may be ready physically, but they are not mature enough mentally. The male is definitely too confused with his hormones to be a good breeder right now. I would split the birds up, do not give either bird a nest – a nest is only for when they are breeding – and give them about 8 months to get more mature and for the male to settle down some.
When they are older you can re-introduce them and try again. Do not give them the nest box right away. See how they act, and if they start to sit together, feed and groom each other, and mate, then you can give them the nest box. For a nest, they need a wooden box – you can do a search for a cockatiel breeding box to find the right type. They do not use an open nest. The box will have a single hole they will use to go in and out of the nest box. The box should be attached to the outside of the cage as high up as possible – your cage may have a breeding door or you may have to cut a hole in the cage to accommodate the nest box.
If the male is still aggressive towards the female when you re-introduce them, then you need to separate them for good and find a different male. Not all birds will make good breeders and not all birds will get along. But when a male acts like your male, it is usually a problem with that particular bird and he should not be paired with another female. He has already destroyed eggs and killed chicks, and this can become a habit. Hopefully he will settle down after having a few more months to mature, but he may simply not be a good breeder bird. All you can do is wait and see how he acts in 8 months.
Thank you for asking Lafeber,
Brenda