No thats perfectly normal, this is not molting, its called preening, they do that a lot, they rub their back (preening gland) and preen their feathers. The small soft grey feathers that fall are normal, this is how the big feathers grow, you will get used to that. About sneazing, are you sure shes not in a cold drift area, greys like warm weather, just be sure shes in a warm spot at the house.
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