Are the pink or thick yellow discharges that appear after an injection to induce menstruation, and which sometimes stop, considered yellowish or brownish discharges (Ṣufrah and Kudrah) that necessitate prayer or prevent it?

These discharges that you see during the time of your period—whether yellowish, brownish, or light red—are considered menstruation according to the preponderant opinion, based on what Al-Mardawi stated in Al-Insaf: "Yellowish and brownish discharges during the days of menstruation are considered menstruation. This is the madhhab (definition), and the companions of the madhhab hold this view."

Therefore, these discharges are treated as menstruation, meaning one refrains from prayer and other acts that require purity, as long as they occur during the accustomed period, until one sees the usual sign of purity, whether it is complete dryness of the area or the discharge of the white secretion.