How to prevent bird mom from abandoning chicks and ensure survival?

You can clean out the nesting box as needed. Gently scoop the chicks out and place them in a clean temporary box. Expect mom to complain and peck. Scrape the box and fill with clean nesting material. Return the chicks to the box afterwards. If the hen is not feeding them adequately, you will need to supplement​ them or pull them for handraising. Use a commercial handfeeding formula. Follow label directions. If you don't have experience hand feeding, ask your avian veterinarian or an experienced breeder. If this is Boo Boo's first clutch, the loss of some of the chicks may be due to inexperience.

Momma bird may be a bit stressed out now that there are new babies to care for. Adding in extra food and water dishes so that each bird has one to eat at without fighting, and making sure both birds have their own perches to relax on can help reduce tension. As for the babies, momma bird should care for them herself, however having some commercial baby bird food (most pet stores will carry it) can be useful in case she can't care for them all on her own. As they get a bit older and start to explore, you can start to offer treats and pets to get them used to being handled.

Thanks for reaching out about Sky. Mother birds sometime can reject babies due to stress or illness. Mother birds can sense the baby is ill or not worth the energy expenditure to raise. The baby might need to be removed or assisted in feeding, for it to survive. Providing heat support might give support but is not a cure. Good luck.

Feed a good quality pelleted diet (Harrison's, Roudybush, Lafeber, Pretty Bird or Exact) supplemented with a fortified seed mix and fresh greens and vegetables. Provide a cuttlebone or mineral block. Always have fresh water available. Provide an appropriately sized nesting box and suitable nesting material (straw, Aspen shaving, shredded newspaper, etc.).

If the chick is 3-5 weeks old, he can be removed from the cage. Use an appropriate hand feeding formula and feed 2-3 times daily. The formula should be warm (not hot) as most chicks will refuse cold food. He should also be kept warm. A cold chick will not eat. By 7-8 weeks, he should be eating seed, pellets and other foods on his own.

As long as the parents are caring for the babies, I would leave them to do their own thing. I wouldn't move or touch the nest while the babies are still young. Once they're a bit older and moving about, you can then clean the nest, or clean it in between clutches. Having baby bird food and a syringe on hand is always a good idea in case you need to step in, notice they aren't thriving or growing well, or the parents aren't caring for them.

As long as the parents are taking care of the hatchling themselves, you shouldn't need to do anything as they will keep it warm by laying with it in the nest, and feed it as needed. It also seems like you are feeding lots of nutrition-filled items to your birds as well! It is a good idea to have some baby bird food and a syringe on hand that you can mix up if you need to help with feeding, or if the parents aren't caring for it. Most pet stores carry this and will have feeding instructions on the side of the bag. Congrats on the baby bird! It sounds like it and its parents are in good hands.