Is it permissible to take money in exchange for supplicating for someone on the condition of their recovery or the fulfillment of their request? And does supplicating for the death of an oppressor and their subsequent death fall under intentional killing as stipulated in the Qur'an?

It is permissible, according to Sharia (definition), to offer a reward ( جعل ) to a Raqi (exorcist/healer) for a cure, based on the Hadith (definition) of Abu Sa'id Al-Khudri regarding the Ruqyah (definition) (exorcism/healing incantation) for the stung person and the acceptance of the reward. This type of contract is a Ju'alah (reward-based contract) and not an Ijarah (definition) (lease/hire contract). Ju'alah is valid for an unknown work or one whose completion cannot be fully guaranteed, such as healing, unlike Ijarah, which requires a known and measurable work. Some scholars also permitted Ju'alah for Du'a (supplication) after reciting the Quran or when visiting the grave of the Prophet (peace be upon him), considering that the reward is for the Du'a and God's response to it, and not for the recitation itself. As for supplicating for someone's death, it is not considered premeditated murder, and there is no sin in it if it is rightful; otherwise, the supplicator would be sinful.