Is not the grave included within the mosque, and if that is the case, how do we reconcile this with the prohibition of building mosques over graves, especially since the grave predates it and the expansion came later? And was it not more appropriate not to include the grave within the expansion?

The Prophet's Mosque was built during the lifetime of the Prophet, peace and blessings be upon him, and was not built over his grave. Rather, the Prophet, peace and blessings be upon him, was buried in his house adjacent to the Mosque. The Mosque was expanded during the time of Umar and Uthman, may Allah be pleased with them, but this expansion did not include the houses of the Prophet, peace and blessings be upon him, which contained his grave. The first expansion that included the houses was in the year 94 AH, and some of the Companions and Tabi'un (such as Sa'id ibn al-Musayyab) disapproved of that. The grave is not inside the Mosque even after its inclusion; rather, it is in an independent chamber surrounded by three walls, and its wall is angled away from the Qiblah.