Is the questioner obligated to break her fast and make up for what she has fasted, or should she continue fasting and praying, given that she used "Primolut" pills to stop her period, and then experienced slight bleeding that continued for thirteen days, while her natural period ranges between ten and eleven days?

If the duration of the blood exceeds one day and one night (the minimum period of menstruation) but does not exceed fifteen days, then it is menses, which necessitates abstaining from fasting and prayer, and making up the fast after performing ghusl. If its duration exceeds fifteen days, then you are experiencing istihaadah (non-menstrual vaginal bleeding), and you should refer to your previous habit; anything beyond that is considered istihaadah.