How is it possible to fast the Day of Arafat, the first ten days of Dhu al-Hijjah, and the voluntary fasts, as well as Ramadan, while adhering to the fast of the Prophet David, peace be upon him (fasting every other day)?

The fasting most beloved to Allah is the fasting of Dawud (peace be upon him), where he would fast one day and break his fast the next. If the day he is supposed to break his fast coincides with days for which fasting is sunnah, such as the day of Arafah or Ashura, then it is better to fast them, and this does not diminish the virtue of fasting one day and breaking fast the next. However, if it coincides with the month of Ramadan, then it is obligatory to fast the entire month, and it is not permissible to break the fast except with a legitimate excuse.