Is it permissible to use Zakat funds for building hospitals and mosques and sponsoring orphans, and is this better than the legitimate uses [prescribed by Sharia]?

The fundamental principle of Zakat is that it is impermissible to disburse it except to the eight categories mentioned in the Quran. Therefore, it is not permissible to spend it on building hospitals or mosques. As for sponsoring orphans, Zakat may be disbursed to them if the orphan is poor or possesses one of the characteristics of those eligible for Zakat.