Is it obligatory to repeat the prayer after the appearance of a blood stain following purification and resuming prayer, then the bleeding stops again and purification and prayer are resumed, and what is the solution in this case?

Do not rush to perform ghusl (definition) after menstruation until you are certain of its cessation, either by seeing the white discharge (al-qassah al-bayda') or by dryness, as the women companions of the Prophet used to do. If you have purified and seen one of these two signs, and then blood appears afterward, it is irregular bleeding (dam fasad) which does not prevent fasting or prayer. If you abandoned prayer or fasting during that period, you are obliged to make up for them.