Do my deeds and fasting become invalid due to my feeling of despair from the mercy of Allah after a discussion with my father and my intrusive thoughts that I am disobedient and despondent, and must I re-fast that day?

All that the questioner mentioned does not affect the validity of the fast, nor is she required to repeat that day. All of this stems from the whispers (waswas) whose cure is to disregard them and pay them no attention. She must strive against herself to repel these whispers and not give them any importance, for they are from the wiles of Satan. She is upon good so long as she strives against them, and nothing from these whispers will harm her.