Is it permissible to curse a person, whether living or dead, and is it permissible to rejoice and pray for Hell upon the killing of one of their soldiers?

It is not permissible to curse a believer, whether alive or dead. A living disbeliever should not be cursed because there is a possibility of his repentance, but if he dies upon disbelief, then it is permissible to curse him. There is no disagreement regarding the permissibility of cursing disbelievers in general, or those among them who died upon disbelief. There is no harm in cursing someone whose death upon Nusayriyyah is certain, because they are more disbelieving than the Jews and Christians. As for the living among them, they should not be cursed, but it is permissible to supplicate against them. It is permissible to rejoice at the killing of enemy soldiers because their evil has ceased. It is better to avoid excessive cursing because it may lead to cursing someone who does not deserve it.