Is it permissible for a Muslim to offer condolences to a non-Muslim, and is a Muslim woman obliged to enter a church or go to graves to participate in the burial of her non-Muslim father?

It is permissible to offer condolences to a disbeliever for their deceased, by saying: "May Allah compensate you (for your loss)." However, it is not permissible to accompany their funeral procession, as this entails glorifying them and purifying them, unless there is no one among the disbelievers to bury them, in which case it is permissible for a Muslim to bury them.

Accordingly, there is no harm for the wife or Muslims to visit her family and offer them condolences, but it is not permissible to enter the church with them on the day of burial or to participate in burying the disbeliever and following their funeral procession.