Will the supplication of an elderly man be answered—who, due to a disagreement and raised voices between them, invoked a curse upon another person, asking God not to grant him success in his life—given that the one cursed is now experiencing intense anxiety and fear that the supplication will come true, and has sent an apology message, though he does not know if it was read or not?

Raising one's voice at an elder contradicts showing them reverence. If you raised your voice in a way that caused him distress, you have wronged him. He has the right to supplicate against you because he is wronged, and the supplication of the wronged is answered. You did well by apologizing to him, and you should frequently supplicate for his well-being and ask Allah for protection from all tribulations.