Is raising one's voice at one's father and quarreling with him a major sin that necessitates repentance, and how can divine forgiveness be attained?

What happened with raising your voice at your father and quarreling with him is considered disobedience (Uqūq), and it is a major sin. Your father's right to kindness and good treatment does not fall, no matter how badly he behaves. Regret for that action is good, and it must turn into sincere repentance (Tawbah Nasūh). There is no need to overreact to your father entering the room or using the computer; you can safeguard your privacy. However, his bringing his friend into the room, if not for a need, is inappropriate. You can come to an understanding with him gently and kindly, and be careful not to fall into disobedience in the future.