What is the ruling on offering condolences to a non-Muslim with phrases like "May God compensate you with your well-being" or "May God have mercy on his soil" to avoid praying for mercy upon him, and is it obligatory to offer condolences to his relatives upon his death?

Offering condolences to disbelievers for their deceased is permissible, and it is permissible to supplicate for a disbeliever regarding worldly benefits, such as bodily health. However, it is not permissible to ask for mercy (i.e., pray for their salvation) for a deceased disbeliever.