Is it permissible for a Muslim to supplicate for his non-Muslim friend, and what is excluded from this supplication, such as guidance, or healing for the sick, or ease of childbirth for the pregnant woman?

It is not permissible to supplicate for a disbeliever with forgiveness or mercy, or similar rewards of the Afterlife; because it is forbidden by the text of the Qur'an and by scholarly consensus. However, it is permissible to supplicate for their guidance and their entry into Islam. As for supplicating for them with worldly benefits, it is not permissible if they are in a state of war [against Muslims]; otherwise, there is no harm in it.