Is a person considered a Muslim merely by performing prayer, even if they do not regret the disbelief they committed and do not resolve not to return to it, taking into consideration previous fatwas that stated that prayer establishes one's Islam?

My advice to the woman is to ignore whisperings (waswas) and to occupy her time with learning, da'wah (inviting to Islam), dhikr (remembrance of Allah), and seeking refuge with Allah from Satan. The repentance of an apostate is by uttering the two Shahadahs (declarations of faith), unless their apostasy was due to denying an obligatory act of worship, in which case their repentance is by uttering the two Shahadahs along with acknowledging the denied obligation. Regret is evident from the questioner's state, and general repentance is valid even if one does not recall specific sins, provided the intention is for general repentance. As for the husband, if he was ignorant of the prohibition of what he did, he does not disbelieve by his action, because a legal ruling does not bind a person until after they have been informed (of it), and he is obligated to learn.