Are the fasting and prayers of a woman who experienced light brown bleeding for two days during breastfeeding, and considered it استحاضة (istihada) based on a doctor's consultation, valid, knowing that she does not remember the number of days she fasted and prayed after that?

Brown discharges (Al-Kudrah) are not considered menstruation unless they are connected to blood at the end [of the menstrual period], or if they occur during the habitual period.

Accordingly, the brown discharges you saw are not considered menstruation but rather irregular bleeding (Istihada), unless they coincide with your habitual period, in which case they would be menstruation.

If it is irregular bleeding (Istihada), you are not required to perform ghusl (ritual bath) after its cessation. You should fast and pray, performing ablution (Wudu') for each prayer, and you are not required to make up any fasts.

If you are considered menstruating, you only need to make up the days of the discharges. Performing ghusl from menstruation is not a condition for the validity of fasting. However, according to the majority of scholars, you must make up the prayers you performed without ghusl, and making them up is more cautious.