The building called Kümbet Camii (Mosque with a dome) straight ahead started life as the Church of the Apostle when it was built in 932-935 for King Abas of the Bagratid. It was turned into a mosque in 1579 when much of the city was rebuilt by the Ottomans. The Russians added the weird looking porches in the 19th century. On its drum are representations of the 12 apostles. I am not certain if it is still used as a mosque.
From the Enc. Britt.: Bagratid: princely and royal dynasty founded in Armenia and Georgia during the 9th century by the Bagratuni family. The Bagratid kings kept Armenia independent of both the Byzantine Empire and the Abbāsid Caliphate. The Bagratids of Ani bore the title of shahanshah (“king of kings”), which was first conferred by the caliph in 922 upon Ashot II the Iron. In 961 Mushegh, the brother of Ashot III, founded the Bagratid kingdom of Kars. By the 11th century, the combined invasions of the Seljuk Turks and Byzantine conquests in the west destroyed what remained of the Bagratids and the Armenian kingdom.
I took pictures inside (couldn't when visiting 6 years before) when I made good taking pictures of the outside, but do not quite know what I took them off precisely.