It's hard for me to say. A lot depends on how much time you have to tend to her. If you think she is suffering at any time, you could put her down to prevent that. I'm sorry that she has not improved.
No, don't give antibiotics to the others unnecessarily. Get Tylan50 injectable, and give it orally. Dosage for a little chick would be 1/8 to 1/4 ml twice daily for 5 days. If using Tylan powder in the water, dosage is 1/4 tsp per quart of water or 1 tsp per gallon, and treat only her for 5...
Did the chicks come from a breeder? The chick could be just very weak from something such as a heart problem, or it could have been exposed to a respiratory disease from wherever it was hatched. Chickens get viruses, bacterial diseases, and fungal diseases. I would continue to give it...
That is good to hear. Most chicks scratch a bit, and it probably is her feathers coming in. What is their bedding--pine shavings? How does her crop feel, and is she eating a drinking?
Have you checked the temperature? Look the chick over that is scratching, in case there is some reason such as tiny bugs. Too much heat can really be a problem. Or it could be too cold. A cheap room thermometer is all that is necessary. Good luck.
What is your brooder temperature with a thermometer on the floor under the lamp? The temperature should be between 85 and 90 degrees F at her age with cooler spot to get to. Make sure that your ventilation is good, and use only pine shavings, paper towel, or sand in the brooder. Try some...