Is it permissible to fast for many days to expiate sins, given the existence of Hadiths that prohibit fasting for more than three days a month or recommend the fast of David?

It is not correct that one cannot fast more than three days, or be limited to the fast of David (peace be upon him). Rather, the matter is broad, and it is permissible to fast less than three days or more. Several hadiths indicate this:

1. The hadith of Abu Qatadah Al-Ansari, which shows the permissibility of fasting the Day of Arafah, which expiates the sins of the past and coming year; fasting the Day of Ashura, which expiates the sins of the past year; fasting three days of every month along with Ramadan, which is like fasting a lifetime; fasting on Mondays; and fasting on alternate days (the fast of David), among others.

2. The hadith of Abu Ayyub Al-Ansari: "Whoever fasts Ramadan and then follows it with six days of Shawwal, it is as if he has fasted a lifetime." This is evidence for the permissibility of fasting more than three days.

3. The hadith of Aisha (may Allah be pleased with her): "The Messenger of Allah (peace be upon him) used to fast until we would say he does not break his fast, and he would break his fast until we would say he does not fast. I never saw the Messenger of Allah (peace be upon him) complete the fast of an entire month except Ramadan, and I never saw him fast more in any month than in Sha'ban." This indicates that fasting is not restricted to a specific number.