My zebra finch father died. Can the mother raise chicks alone?

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.

It sounds as if your female may be sick and it would be best to bring her to a vet ASAP. It is possible she is exhausted from laying the eggs due to malnutrition, has an illness, or even has a stuck egg that is making her ill. Seeking veterinary care in person ASAP is best to try and get her feeling better. You may also need to separate her into a warm hospital cage until you can get to the vet to help make her more comfortable and reduce stress.

If she hasn't mated and raised young before then I would say 2 may be too old for a zebra finch for her first clutch. But if she is already raising young she can continue for another couple of years. I would try to limit her to 2-3 clutches a year. Zebra finches usually live 4-7 years in captivity though some have been known to live longer. https://vcahospitals.com/know-your-pet/finches-general

As long as he/she is eating, drinking and behaving normally otherwise, there is no cause for concern. Given time, the behavior will go back to normal. You can help by decreasing exposure to daylight and by lowering room temperature a few degrees.

if you took the chicks away that early to begin hand-feeding and taming, having them where the parents can see/hear may help them calm down some. Otherwise, adding in some extra toys and treats for your female to interact with may help her a little. However, it may just take some time since she was busy caring for her babies and probably doesn't understand why they were taken away.

When zebra finches are all white it is sometimes hard to tell if they are male or female as they won't have the characteristic cheek markings, beak coloration or tail patterns. The two pictured look like they could possibly both be female, but it is hard to tell due to the distance from the camera and the lack of markings present (males will sometimes still have darker cheek areas, a stripe on the cheek, or a darker red beak). Males will also sing almost constantly that sounds quite different than regular chirping, and will also "tail waggle" when they are wanting to/attempting to mate with a female. If none of your birds are doing this, it is possible they are all female. Both males and females will show interest in nests and will go in them to sleep at night even if they aren't raising babies. If one is being left out, you can add in another nest or sleeping area to see if it helps.

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.