Can a Muslim's supplication repel hurricanes, earthquakes, epidemics, and tribulations, and how would such a supplication be made?

Yes, supplication (Du'a) repels affliction (Bala'), and this has been established in the prophetic Sunnah (definition). It lifts calamities, earthquakes, tribulations, and epidemics. It is preferable for the supplication to be with what has been ورد in the Shari'ah, and it is permissible with other wordings as long as they do not contain a Shari'ah prohibition. Among the etiquettes of supplication are: supplicating by Allah's names and attributes, having a present heart, seeking out times of response, facing the Qiblah, being in a state of purity, praising Allah and sending blessings upon His Prophet, not raising one's voice, freeing oneself from injustices, drawing closer to Allah through charity and acts of obedience, and consuming lawful earnings. We advise referring to books of authentic supplications.