Is this place, where the five daily prayers and Tarawih are observed, and lessons are held, and which has a resident Imam and a board of directors, considered a mosque with its rulings, or merely a prayer area?

Linguistically, a mosque (masjid) is a house of prayer and a place of prostration. Technically, it is every place built for the prayer to Allah, or every place where Allah can be worshipped and prostrated to. Customarily, it specifically refers to a place prepared for the five daily prayers. The Malikis and Shaykh al-Islam held that if a place is designated as a waqf (endowment) to be a mosque, the endowment is valid, and it becomes a mosque, thereby acquiring the rulings pertinent to a mosque. In contrast, the majority of scholars believe that a place rented for prayer does not take on the ruling of a mosque because it is not a waqf, and it cannot be made a waqf unless it is owned.