When you interpret dreams, you need to think in terms of all the characters being part of yourself. The details of the characters in terms of colors, directions, actions, etc. , give us more detail about our inner world. This is subtle so let me explain.
Say you are in a good relationship with someone special, and you feel happy and light when you are around that person. One day, they go away and you never see them again. This can make you depressed. The person that made you happy, in real time, pushed certain buttons within your mind and heart, which is why you felt that happy lightness. When they left and the these buttons were no longer being pushed, the emotions change. These triggers and memories are all within your mind. In a dream, that person would reflect that consolidated part of your own personality/brain, that is being activated, due to the impact of that person. The person in the dream symbolizes their own impact within you; reflection in the mirror of your mind.
In the dream, the dad who was dead, and appears in the dream. He symbolizes those old feelings and reactions, which were once activated by dad. These dynamics appear again, since they are in memory and never really die. They only lack the external trigger needed to remain active. In the dream, dad is talking normal since he is there in memory, yet you feel the need to speak loud, since he appears a distant memory. Taking inventory means to make note of the buttons being pushed, since his image of love and joy is still there within you. If you think back at a good time and thereby trigger the memory grid yourself the buttons are pushed again since dad is part of you.