What are the necessary criteria for a place to be considered a mosque, and is praying in a place where the five daily prayers are regularly performed, but which does not meet all the conditions of a mosque, like praying at home?

A mosque is a place dedicated to Allah, where general permission has been given for prayer, and it is prepared for the perpetual performance of the five daily prayers. It ceases to be the property of its owner. As for a musalla (prayer room), it is a place taken for an occasional prayer, and it has not been dedicated for the five daily prayers, nor is the "tahiyat al-masjid" (two rak'ahs upon entering a mosque) prayer prescribed for it.