Do intermittent bloody discharges after inserting an IUD affect the validity of prayer and fasting, and does the menstrual period change because of them?

This blood, which returned after five or six days of cessation, is not considered menses, because it occurs at a time when it cannot be menses. If it is confirmed that you are experiencing istihada (non-menstrual bleeding), then you should refer to your previous habit. If your habit has changed and settled at ten days, then your latest habit is what is considered, and anything else is istihada. Therefore, you should not pay attention to any bloody discharge you see outside of your habitual time.