Is what the questioner did—considering herself in the status of one experiencing Istihada (non-menstrual vaginal bleeding)—correct? And what are the implications for her regarding making up missed prayers or offering expiation, knowing that the brownish discharge and bleeding she observed continued after her surgery to remove a fibroid, and her regular menstrual period is seven or eight days?

The brownish discharge you first saw is not considered menses unless it occurred during your regular period. The same applies to brownish discharge seen after cessation (of bleeding). As for the blood you saw, which lasted for ten days, all of it is considered menses. Therefore, you were not permitted to fast or pray during that time. You are obligated to make up all the days you saw blood, as well as the days you broke your fast when you saw the brownish discharge, assuming it was menses. Regarding your health condition, its ruling is to be referred to medical specialists.