Thank you for waiting. The box with a heating pad is not a good idea. Parakeets usually lay their eggs in a nest box, which you can buy at larger pet stores. Parakeets generally lay between 4 and 8 eggs in a clutch. The female will sit on the eggs, after the clutch is complete. The eggs do not need to be warm until then. Keeping eggs warm artificially is likely to result in no chick hatching. That's because the mother's body provides exactly the right amount of heat and humidity to hatch the eggs. If you don't have a nest box in her cage, you'll need to get one as soon as possible. Put the two eggs in it, and then leave them alone. Here is an online source for a nest box:
Here is where you can find plans to build one:
You don't need to do anything to care for the eggs - the parents will take care of that. You shouldn't touch or handle the eggs. Don't remove the dad. He'll take care of his mate while she's sitting on the eggs, and may assist with the babies when they hatch. The eggs should start hatching in 17-20 days from the day the female begins sitting on them. They won't all hatch on the same day.
Your main job for awhile will be to make sure there's plenty of nutritious food available, and that the cage is kept very clean, but don't clean the nest box until the babies are older. As the babies get older, you'll have more to do. Here's a link to a site that will tell you about feeding, how the little ones will develop, how to tame them, etc.
The other thing you need to be aware of is that many times, a parakeet's first clutch will not be fertile, even if you saw them mate. If they don't hatch by 21 days after the female began sitting on them, they are infertile and should be removed. Most birds will start a second clutch then. Raising baby birds is not all pleasant. These things may not happen, but you just need to be aware that they are possibilities. It's common to have some babies die even after they hatch. A baby can hatch with deformities. Some inexperienced parents won't do a god job of caring for them. Some may even hurt or kill their own babies. I hope none of these things happen to you, but if they do, it doesn't mean you did something wrong. When breeding any kind of bird, we have to be prepared for any possibility.
Be sure to provide a high quality pelleted feed for the parents, along with some seeds, and fresh produce. Little pieces of boiled egg are also good. It's also important to be sure there is both a cuttlebone and a mineral block available for the female. Producing eggs takes a lot out of her body. Inadequate foods or calcium increases the chances that she could become egg bound or lay deformed eggs.
In summary, I recommend that you read the information on the site I gave you a link to, provide a nest box with pine shavings in it, place the already laid eggs in it, and then leave the nest alone, and let the parents handle it. If you have more questions, just let me know. I hope everything will go smoothly, and you'll soon have some babies to enjoy.
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