Is it permissible to build mosques or hospitals with Zakat funds, and is that considered spending the money of the poor?

Allah Almighty has restricted the eligibility for Zakat to the eight categories mentioned in the 60th verse of Surat At-Tawbah. This does not include building mosques, hospitals, or similar charitable projects, as the most preponderant opinion is that the phrase "fi sabilillah" (in the way of Allah) refers to jihad.