Why are the baby birds I'm feeding screaming and biting?

Their diet in the wild is mostly insects and berries, so purchasing some live crickets from a local pet store, or some berries from your store and offering them may help get them used to what they would forage for in the wild as they get weaned off the kitten food (and can be fun to teach baby birds how to catch food with live insects.) If there isn't a wildlife rehab nearby (India does have several), you can also see if there is a vet or group in your area that does wildlife rescue that may be better equipped for caring for the birds and releasing them back into the wild once they are old enough.

You can definitely try to feed it, you will need to buy wet canned cat food such as Recovery or A/D (from your local vet) as well as a syringe, you will need to feed it every couple hours during the day (no need to feed during the night).

First time and young parents may not know what to do with a baby and may need assistance from you. It may also be that she is still focused on the unhatched eggs instead of the baby. Purchasing a syringe and some baby bird formula (most pet stores will carry this) is best. The formula should have instructions for how much to feed and how often depending on your bird's size, age and breed, however most baby birds will need to be fed frequently. You can check how full they are by looking at the crop, which is a sort of "balloon" just under the chin that is usually more visible before their feathers come in-- when full, it will fill up, and when hungry it will be empty. If the baby doesn't seem to be getting fed enough, stepping in with supplementation can help. If the mother and father are picking on the baby heavily, or kicking it out of the nest completely, you may need to move him to a separate cage that is kept warm with a nest and heat lamp, and provide all feedings yourself.

It looks like it may indeed be of the Warbler species. These birds typically eat insects, so small crickets or mealworms would be recommended. Ideally, you should contact a local wildlife rehabilitator for assistance. A rehabber will have the knowledge and experience to give the bird the best chance at eventual release.

The best solution would be to contact a local wildlife rehabilitator. One in your area specializing in avians should be able to identify it. The bird looks to be healthy, so you've been doing a good job. The rehabber can confirm this then let you know when the bird can be released. Search online, contact a local veterinary clinic or check the California Department of Fish and Wildlife website to find a rehabilitator.

It is possible he/she may have aspirated some food into the lungs. This can lead to respiratory infection or even pneumonia. The bird should be examined by a wildlife veterinarian or a vet experienced in treating birds.

His best chances will be to stay with his parents. If you can see where the nest is, you may briefly pick him up to place him back in the nest. Most birds do not actually have a very good sense of smell, so your scent won't cause a problem - however, your presence will frighten the parents away. If you cannot return him to the nest, the best course of action depends on how old he is. If he's got feathers and can hop, he's probably a fledgeling who is learning to leave the nest and you should leave him alone. If he's just starting to get his feathers and seems bright (can lift his head and look around), make sure he's in a safe spot (you can make a little nest on the ground with a clean towel in a small box - but don't move him far from where you found him, so his parents can find him there too) and see if the parents come to feed him. If you're convinced he's on his own, or if he's too little to have any hope of surviving on the ground (even if the parents stop by to feed him), then I recommend finding your closest wildlife rehab location and calling to see if they'll take him. Hope this helps!