Hi there and
to Talk Budgies!
It's great to have you here with us; you couldn't have come to a better place to learn even more about these beautiful birds!
However, owing to the fact that you do not yet know enough about budgies to be able to breed them safely, it is best that you immediately check if the eggs are fertile, and if they are not, discard them. This does not harm any life, if the eggs are infertile, it is just the same as throwing away a chicken egg from the grocery store. After throwing away the egg(s), totally rearrange the cage, and if the female is still showing signs of wanting to lay, separate her from her male budgie for a while, until she comes out of breeding condition.
If the hen's eggs are fertile, then you're going to have to help her through this. Be sure to read through all the breeding stickies, which will answer a lot of your questions.
As for her runny poops, when hens lay eggs, they often have very large and runny poop. If in a few days, this doesn't clear up, you must take her to the vet or she may not live, endangering the lives of any chicks she may have, other than her own.
Deciding to own budgies comes with the dedication to their vet care, and while I know that it's not your fault that your parents do not want you to spend money on that, it is your responsibility to find a way to take her to the vet if she needs it. Additionally, if she does raise chicks, you also need to have access to an avian vet as they are the only ones qualified to treat very young birds. Save your pocket money, or try and get a job to save up for a visit to the vet, whether it's for your female now or for the future when you do need to take them.
Additionally, be sure to look through the forum's many Budgie Articles and "stickies" (threads "stuck" to the top of each subform for easy reference) to stay up to date on all the best practices for caring for budgies. If you have any questions after reading through anything, be sure to ask as we'd love to help!
Best of luck, I hope everything goes well!