Do rented premises designated for the five daily prayers and Friday prayer take the ruling of a mosque, and is trade permissible therein for the purpose of covering part of the rent?

A prayer area (musalla) does not have the same ruling as a mosque. It is owned by individuals and may be sold. A menstruating woman is permitted to stay in it. The prayer of "greeting the mosque" (tahiyyat al-masjid) is not prescribed for it. However, performing sunnah prayers in it is permissible. Selling booklets and commercial advertisements in it is inappropriate because it distracts from the remembrance of Allah and disturbs those who are praying.