Can a wife lead the prayer when praying with her husband at home, and what are the conditions that must be met by the one leading the prayer, the invalidation of which would invalidate the prayer itself?

The basic principle is that a man should call the Iqamah (call to commence prayer). However, if a woman calls the Iqamah, there is no harm according to some scholars. Others have said that a woman's Iqamah for a man is not valid.

It is recommended for the one who calls the Iqamah to meet the conditions that are recommended for the Mu'adhin (caller to prayer), which are: purity, facing the Qiblah, standing, and having a good appearance. If these conditions are not met, the Adhan and Iqamah are still valid, though disliked.

The prayer is not invalidated by omitting the Adhan or the Iqamah, because they are Sunnah acts performed outside of the prayer itself.