Is it permissible for my father to collect Zakat money to build a mosque, based on a fatwa he heard?

Zakat has specific categories of recipients mentioned in the Holy Quran, and it is not permissible to disburse it for purposes other than these. The category "Fi Sabeelillah" (in the way of Allah) is specific to jihad according to the majority of scholars. Therefore, it is not permissible to spend zakat on building mosques. This opinion is almost a consensus among jurists, and they base it on two points: first, that a mosque cannot be owned, and second, the restriction of the eight categories in the verse, among which mosques are not included. If the verse were interpreted to include every righteous deed, then the restriction would lose its purpose, and those who are undeniably deserving of zakat would be deprived. Therefore, zakat must be disbursed according to its legally designated categories.