My thought process, where have I gone wrong?
Question 1: There is no gravitational force at the center of the earth is there still gravitational time dilation. Answer: Yes, there is a potential difference between the center of the earth and the surface, so according to general relativity the center will be slightly slower than the surface.
Question 2: Does all the mass in the observable universe have an effect on local gravitational potential and thus cause noticeable local time dilation? Answer: Yes and No. Think about the observable universe as a very large low-density sphere. As you move outward in this sphere, the area thus mass increases in proportion to r^3. This overpowers the inverse square law of gravity, so time is significantly slowed. However, everywhere has its own sphere so the universe affects everywhere equally, as a result, there is no noticeable local change.
Question 3: Is the local time dilation currently changing? Answer: Yes. The universe is expanding, thus the mass of the universe is moving further away, this overcomes the observable universe expanding. This means time is currently speeding up.
Question 4: If time is speeding up does this mean when we look at distant objects we are looking into the past thus when time is slower? Answer: Yes. Distant objects will be slower and red-shifted. This will make it look like the universe is expanding at an accelerating rate.
Question 5: Does this mean the theory of dark energy is incorrect? Answer: ??? I must have made a mistake somewhere. Ask the internet.