Is it permissible to consider a place designated for congregational prayer in the home as a mosque, such that one prays تحية المسجد (two rak'ahs upon entering a mosque) in it, and awaits the call to prayer even during times when prayer is ordinarily forbidden?

There is no objection to establishing a prayer room (musalla) in the house where the call to prayer is made and prayers are performed with the family. This was a practice common among the righteous predecessors and is supported by the Sunnah. However, these prayer rooms do not take the ruling of a mosque because they are not endowed for the general Muslim public. Ibn al-Arabi said: "If a man builds a mosque in his house, and restricts it from people, and dedicates it exclusively to himself, it remains his property, and does not attain the status of a mosque." Furthermore, they do not take the ruling of a mosque in terms of prohibiting menstruating women from entering, performing the salutation of the mosque (tahiyyat al-masjid), or prohibiting the announcement of lost items.