cockatiels usually become sexually mature around 1 year old, like humans it can vary a little bit(some at 8 months others a little older) but that said it's still not healthy, I can only assume your bird was egg bound since(if I read the post right) she laid two eggs in one day, tiels typically lay one egg every other day till their brood is set, I doubt that hard boiled egg will help her tiels share parenting responsibilities, with her rejecting the male she wont have the support and will likely become thin as a result, another concern is a lack of calcium.
another problem that arises with tiels is that they can lay continuously for years, once they start it's tough to get them to stop, read down through the posts on this forum, infact the post right under this thread titled "excessive egg laying" is a typical one, they also dont have a "season", they'll usually lay whenever food is plentiful and the daylight hours right, they do have hormonal periods where they become nippy but even males go through this, I dont believe it plays much role in their egg laying and breeding.
also being that this is her first clutch if anything should happen to hatch she probly wont take care of it properly and it's not uncommon for them to abandon a single chick if there are no other eggs to hatch.
I breed budgies, my pairs first clutch of 6 eggs 4 chicks died off one lived for 2 weeks then the younger of the two passed and she abandoned the oldest one, the chick didn't take to hand feeding since his eyes had opened, breeding any bird takes alot of work, knowledge and commitment.