What is the ruling on fasting and prayer in the mentioned case, and what is the distinction between menstrual blood and abnormal bleeding (Istihada), and what is required for the days she did not fast, believing it to be menstruation?

What became clear is that what the questioner saw of red veins and brown spots is not menses, because it appeared before the usual time of her period and does not carry the usual characteristics of menses. Her regular period began on 10/31, so she must make up the days she fasted after this date. As for the period before this date, fasting was obligatory upon her, and she must now make up the days she did not fast. The days she did fast, her fast is valid, but if she makes them up as a precaution, that is better. She must only make up the prayers she missed during this specific period.