Is it permissible to fast the Ayyam al-Bid (the 13th, 14th, and 15th) of Dhul-Hijjah, knowing that the 13th is one of the Days of Tashreeq during which fasting is forbidden, or should these days be compensated for by fasting other days of the same month?

It is not permissible to fast on the Days of Tashreeq except for the pilgrim performing Tamattu' Hajj who cannot find a sacrificial animal. These are the three days following Eid al-Adha. Therefore, it is obligatory to avoid fasting on the thirteenth day of Dhul-Hijjah. However, if a Muslim fasts three days of any month, they will receive reward and recompense.