alicemaiwaifu, you are right, the plane belonged to 586th fighter aviation regiment (ИАП). This women's aviation unit existed from 1941 to 1945 yrs. http://ru.wikipedia.org/wiki/586_иап
It's a Polikarpov I-16 UTI (or UTI-4). If it carries weapons in the wing could be based on a type 10, otherwise could be based on a type 5 or 6. Anyway, lots of these machines were modified from damaged & old planes.