Have you assigned them their names? :D If not yet, I suggest going for Japanese J names for them. These names are short, just like these little chicks, so would suit better right?
By the time her chicks are a month old, she’s most likely done with the whole “mom mode.” Odds are she won’t take the new ones and could even reject or hurt them. Safer to raise them in a brooder.
She should be broody. All that puffing up and sitting nonstop is classic. If there’s no plan for chicks, best to break the cycle and pop her in a wire-bottom cage with food and water, no cozy bedding. That can cools her off and resets things.
Give mama her own little setup, away from the big hens and the 6-week-old chicks. That way the new babies stay safe, and she can focus on being a good mom without all the chaos. Once the chicks are a bit older and can hold their own, slowly introduce them back in.
She could be dealing with a calcium deficiency, infection, or internal issues (egg binding). Keep giving fluids and food. If she doesn’t improve soon, call your vet to check for infections or others.
Oh, spring feather loss can be a light molt, which is normal. Give them protein a bit (mealworms) and check for mites or pecking. If they’re active and eating, they then should be fine!