Is my prayer invalid if I pray with a headband that has become ritually impure? And are my previous prayers, in which I did not use the headband, invalidated? How can I atone for them? And how should the headband be used? And must I repeat all my prayers on a day when I find traces of ritual impurity on my clothes?

The person afflicted with سلس (incontinence) should refer to Fatwa No. 42369 to know what to do if he wishes to pray. The bandage prevents the impurity from exiting and spreading, and what afflicts it is not taken into consideration as long as nothing comes out from its sides due to negligence in tightening it. As for previous prayers in which the bandage was not used, if you were not afflicted with impurity during the prayer, then your prayer is valid. Otherwise, there is no need for you to repeat them according to the Maliki school, or according to those who prayed with impurity forgetfully or ignorantly, as stated by Ibn Taymiyyah.

In the future, the bandage should be tightened as a precaution. Renewing the bandage for each prayer has details mentioned by Al-Nawawi; its summary is that renewing it is obligatory if the bandage moves from its place or if blood appears on its sides. Otherwise, there are two opinions.

Tightening with a bandage is not obligatory if it results in harm. If blood comes out due to negligence in tightening or if the bandage moves, then both purification and prayer are invalidated. The traces of impurity that the questioner finds do not necessitate repeating the prayer because he is excused due to incontinence. There is no expiation required for this matter, but repentance is obligatory if you were negligent.