Is building a mosque, a Qur'anic school, and an events hall on state-owned land that is currently inalienable considered an act consistent with Shar'i rulings, for which the doer will be rewarded, knowing that the land will be documented in the name of Awqaf later?

It is permissible to build a mosque on land owned by no one, especially if the state has established a public project on it and has not prohibited it, particularly if the area is in need of a mosque due to the scarcity or small size of existing mosques. Furthermore, whoever strives to build it will receive reward and recompense.