5 minutes per chick? you are lucky! It takes me at least 1.5 hours for all 4 of them and I try to do it 3 times a day! My life is a hell right now
I don't know why they don't eat. I mean, it seems that they want to, but I am probably that much inexperienced so I can't do it right. If the chick is facing me, and not very wiggly, I do OK. If chick isn't facing me and I am behind the chick, I have to squeeze the formula on the right side of the beak because I am right handed and very uncomfortable doing it on the left side of the beak. Is it not a big issue? Left to right only need to be done with the feeding tube, correct?

They also run away, fly away and just moving their heads so that formula goes in the nose or eye or top of the head. The best result is when I am pressing the chick down tight but then they are forced.

What is my goal for now? Should they keep weight stable? Or Should they gain weight?
Also, its not easy to have enough time for feeding as I have lots of other things to do.
Lady from the store called me but all she can do is giving me advise over the phone. This is not what I need.
We ordered the cage on Amazon.

talking about seiling fan - I hate it! Dad taught them how to sit on it, so all they want to do is sitting on the fan!

It sounds like you need to restrain the babies when you feed them. Put your left hand over the chick's back, tilting it up slightly so you can put your thumb and index finger lightly around the chick's neck. Don't try to hold the baby tight, it won't like that and a loose hold works pretty well. If the baby tries to get away from you by backing up (which is the direction they go instinctively), your hand will be like a wall preventing it from going anywhere. Having your fingers around the head will keep the baby from moving its head around too violently. You need to let it bob its head some because that's the only way they know how to eat, but you can keep the movement a little more controlled.

They are just scared of that pipette! Its probably like trying to feed formula from the bottle to a completely breastfed child. I would say it takes more than one day to break the habit and the mom should be completely removed.
Your advise above didn't work - they wiggle their way out and are very strong! Surprisingly strong for malnourished babies.
I also noticed that dad prefers some chicks to others. The pearl girl always gets fed.
IS it normal for chicks to help other chick to clean? Or is ti beginning of plucking?
One baby learned how to get inside the nestbox and the mom doesn't mind a company. So I am having one more problem - how to get that baby out for anything (handfeeding, out of cage time, eating other food, etc) - the mom attacks me when I put my fingers in.

Chick-restraining takes a little practice, but you're much bigger and stronger than they are so you'll get the hang of it. Is the baby inside the nest being fed by mom? If so, you might be able to just let her take care of it.

Chicks do help clean each other up sometimes. They recognize that the other baby has food on its face and they want to eat it. I've never seen it lead to plucking with my babies.

I have no clue if the baby inside the nestbox gets fed. Too busy trying to feed the rest of them.

I don't know if we should continue the torture of handfeeding. It appears to be the torture for them, and thus, torture for me. Well, sometimes some of them respond, and I have a good feeling after this, but not all of them and not always. For example, Tator Tot, the youngest chick, always behaves like I am executing him. Whatever formula comes in, comes in by accident. He is the one who had the most dramatic weight loss, from the second heaviest to the lightest. Somehow he managed to gain a few grams today, and measured at 81g in the evening which is not bad for him at all (peak was 103g)

Bella, who loves to sit in the nestbox with mommy, has been seen playing with pine bedding or eating it (hard to say). What is the chance she is eating it? Is it common? Is it dangerous?

Sammy, who was born first, LOVES to pick up seeds and crumbs and other food on the cage floor, that's his favorite time-spending, so I am not worried for him.

Stella, the pearl girl, is daddy's favorite, always gets fed by him. She is interested in toys.

A good thing is that our cock, I think, picking up his new responsibilities. It always takes him time to figure out how to behave in different stages of breeding. He is seen feeding the kids more often but still ignores them a lot.

Mom still not feeding anybody and spending a lot of time in the box.

We got the new cage but didn't have a chance to look at it.

The store, I think, don't feed them at all on Sundays (they leave pellets and seeds in cages), which is a bad sign for me. I may be wrong, as they have some really tiny babies without parents in the nursery, but maybe they take this tiny chicks home with them.

DO you think my chicks would benefit from being sold to the bird store or not? As I saw, they feed them several times a day, but don't let them out or handle, also no toys or anything in cages (just feeders and perches).

The new clutch was started Nov 12, and she sat from day 1, so it should be due beginning of December, when the older chicks will be about 6.5 - 7 weeks old. What is the chance parents will continue feeding them? Or should I persist with handfeeding for not leaving them without nutrition if/when the new chicks are born?

Another issue. I noticed that formula gets thinner overtime because my process takes not less than an hour to feed all. I keep cup with formula in a pot with hot water and I have to replace hot water several times, and this eventually makes formula not so dense. I probably need to make a new cup for the last 2 chicks.

I am amazed how fast and how well they learning to fly. I wouldn't even say they were clumsy learning to sit on perches. Sometimes a chick lands on top of another chick and this is probably no fun for the one on the bottom.

IS this OK that my chicks don't bob their heads when I feed them? They just have no chance... If I leave them free enough to bob their heads, they will be gone in no time.

It sounds to me as though the chicks are eating more than you think. They have not starved to death and they have enough energy to fly around and play. One chick is even gaining weight. By this time they must have realized that you are putting food in their beak, but they don't want it. So it's best to not try to feed them so often. Monitor their weight and their behavior, and offer them formula at least once a day so they can take it if they want it. But if they seem to be strong and don't want the formula, don't force them to take it.